The approximation property for spaces of holomorphic functions on infinite dimensional spaces II
Let H ( U ) denote the vector space of all complex-valued holomorphic functions on an open subset U of a Banach space E. Let τ ω and τ δ respectively denote the compact-ported topology and the bornological topology on H ( U ) . We show that if E is a Banach space with a shrinking Schauder basis, and...
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| Vydané v: | Journal of functional analysis Ročník 259; číslo 2; s. 545 - 560 |
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| Jazyk: | English |
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01.07.2010
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| Abstract | Let
H
(
U
)
denote the vector space of all complex-valued holomorphic functions on an open subset
U of a Banach space
E. Let
τ
ω
and
τ
δ
respectively denote the compact-ported topology and the bornological topology on
H
(
U
)
. We show that if
E is a Banach space with a shrinking Schauder basis, and with the property that every continuous polynomial on
E is weakly continuous on bounded sets, then
(
H
(
U
)
,
τ
ω
)
and
(
H
(
U
)
,
τ
δ
)
have the approximation property for every open subset
U of
E. The classical space
c
0
, the original Tsirelson space
T
∗
and the Tsirelson
∗–James space
T
J
∗
are examples of Banach spaces which satisfy the hypotheses of our main result. Our results are actually valid for Riemann domains. |
|---|---|
| AbstractList | Let
H
(
U
)
denote the vector space of all complex-valued holomorphic functions on an open subset
U of a Banach space
E. Let
τ
ω
and
τ
δ
respectively denote the compact-ported topology and the bornological topology on
H
(
U
)
. We show that if
E is a Banach space with a shrinking Schauder basis, and with the property that every continuous polynomial on
E is weakly continuous on bounded sets, then
(
H
(
U
)
,
τ
ω
)
and
(
H
(
U
)
,
τ
δ
)
have the approximation property for every open subset
U of
E. The classical space
c
0
, the original Tsirelson space
T
∗
and the Tsirelson
∗–James space
T
J
∗
are examples of Banach spaces which satisfy the hypotheses of our main result. Our results are actually valid for Riemann domains. |
| Author | Mujica, Jorge Dineen, Seán |
| Author_xml | – sequence: 1 givenname: Seán surname: Dineen fullname: Dineen, Seán email: sean.dineen@ucd.ie organization: Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland – sequence: 2 givenname: Jorge surname: Mujica fullname: Mujica, Jorge email: mujica@ime.unicamp.br organization: Departamento de Matemática, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil |
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| Cites_doi | 10.4064/sm-122-2-139-151 10.5802/aif.419 10.1016/j.jmaa.2006.05.076 10.1007/s13163-009-0026-7 10.1007/BF01419608 10.1016/j.jat.2004.01.008 10.1016/S1385-7258(67)50051-3 10.5802/aif.68 10.1016/0022-1236(76)90026-4 10.1007/BF01351314 10.1016/S0019-3577(01)80022-7 10.1016/0022-1236(83)90081-2 10.1007/BF01078599 10.1090/S0002-9939-1984-0728358-5 10.4064/sm-16-2-173-182 10.1007/BF02385668 10.5802/aif.345 10.1007/BF02392870 10.1216/rmjm/1181071856 |
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| Keywords | Pseudoconvex Riemann domain Holomorphic function Banach space Schauder basis |
| Language | English |
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| References | Gillman, Jerison (bib015) 1960 Bierstedt, Meise (bib006) 1974; 209 Tsirelson (bib033) 1974; 8 Gruman, Kiselman (bib017) 1972; 274 in press Nachbin (bib026) 1970; 271 Boyd, Dineen, Rueda (bib008) 2001; 12 Aron, Hervés, Valdivia (bib004) 1983; 52 Aron, Schottenloher (bib005) 1976; 21 Bogdanowicz (bib007) 1957; 5 Dineen (bib012) 1999 Díaz, Dineen (bib010) 1998; 36 Szankowski (bib032) 1981; 147 L. Schwartz, Produits tensoriels topologiques d'espaces vectoriels topologiques, Applications, Séminaire Schwartz 1953–1954 Schwartz (bib031) 1957; 7 Grothendieck (bib016) 1955; 16 Aron, Dineen (bib003) 1997; 27 Floret (bib014) 1997; 17 Dineen (bib011) 1972; 196 Alencar, Aron, Dineen (bib001) 1984; 90 Pelczynski (bib027) 1957; 16 Coeuré (bib009) 1970; 20 Mujica (bib022) 1997; 122 Hirschowitz (bib018) 1972; 22 Mujica (bib021) 1986; vol. 120 Schottenloher (bib029) 1975 Nachbin (bib025) 1967; 29 R. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, Doctoral thesis, Trinity College Dublin, 1980 J. Mujica, D. Vieira, Weakly continuous holomorphic functions on pseudoconvex domains in Banach spaces, Rev. Mat. Complut. Jarchow (bib019) 1981 Dineen, Mujica (bib013) 2004; 126 Mujica (bib023) 2009; vol. 1 Vieira (bib034) 2007; 328 H. Alexander, Analytic functions on Banach spaces, PhD thesis, University of California, Berkeley, 1968 Lindenstrauss, Tzafriri (bib020) 1977 Aron (10.1016/j.jfa.2010.04.001_bib005) 1976; 21 Hirschowitz (10.1016/j.jfa.2010.04.001_bib018) 1972; 22 Nachbin (10.1016/j.jfa.2010.04.001_bib026) 1970; 271 10.1016/j.jfa.2010.04.001_bib002 10.1016/j.jfa.2010.04.001_bib024 Lindenstrauss (10.1016/j.jfa.2010.04.001_bib020) 1977 Bierstedt (10.1016/j.jfa.2010.04.001_bib006) 1974; 209 Grothendieck (10.1016/j.jfa.2010.04.001_bib016) 1955; 16 10.1016/j.jfa.2010.04.001_bib028 Alencar (10.1016/j.jfa.2010.04.001_bib001) 1984; 90 Aron (10.1016/j.jfa.2010.04.001_bib004) 1983; 52 Pelczynski (10.1016/j.jfa.2010.04.001_bib027) 1957; 16 Szankowski (10.1016/j.jfa.2010.04.001_bib032) 1981; 147 Dineen (10.1016/j.jfa.2010.04.001_bib012) 1999 Vieira (10.1016/j.jfa.2010.04.001_bib034) 2007; 328 Gruman (10.1016/j.jfa.2010.04.001_bib017) 1972; 274 Nachbin (10.1016/j.jfa.2010.04.001_bib025) 1967; 29 Gillman (10.1016/j.jfa.2010.04.001_bib015) 1960 Dineen (10.1016/j.jfa.2010.04.001_bib011) 1972; 196 Schottenloher (10.1016/j.jfa.2010.04.001_bib029) 1975 Coeuré (10.1016/j.jfa.2010.04.001_bib009) 1970; 20 Díaz (10.1016/j.jfa.2010.04.001_bib010) 1998; 36 10.1016/j.jfa.2010.04.001_bib030 Bogdanowicz (10.1016/j.jfa.2010.04.001_bib007) 1957; 5 Boyd (10.1016/j.jfa.2010.04.001_bib008) 2001; 12 Floret (10.1016/j.jfa.2010.04.001_bib014) 1997; 17 Mujica (10.1016/j.jfa.2010.04.001_bib023) 2009; vol. 1 Tsirelson (10.1016/j.jfa.2010.04.001_bib033) 1974; 8 Aron (10.1016/j.jfa.2010.04.001_bib003) 1997; 27 Jarchow (10.1016/j.jfa.2010.04.001_bib019) 1981 Mujica (10.1016/j.jfa.2010.04.001_bib021) 1986; vol. 120 Dineen (10.1016/j.jfa.2010.04.001_bib013) 2004; 126 Schwartz (10.1016/j.jfa.2010.04.001_bib031) 1957; 7 Mujica (10.1016/j.jfa.2010.04.001_bib022) 1997; 122 |
| References_xml | – volume: 36 start-page: 87 year: 1998 end-page: 96 ident: bib010 article-title: Polynomials on stable spaces publication-title: Ark. Mat. – volume: 147 start-page: 89 year: 1981 end-page: 108 ident: bib032 publication-title: Acta Math. – volume: 12 start-page: 147 year: 2001 end-page: 156 ident: bib008 article-title: Weakly uniformly continuous holomorphic functions and the approximation property publication-title: Indag. Math. (N.S.) – reference: J. Mujica, D. Vieira, Weakly continuous holomorphic functions on pseudoconvex domains in Banach spaces, Rev. Mat. Complut., – start-page: 261 year: 1975 end-page: 270 ident: bib029 publication-title: Analyse Fonctionelle et Applications – volume: 20 start-page: 361 year: 1970 end-page: 432 ident: bib009 article-title: Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'etude des fonctions analytiques publication-title: Ann. Inst. Fourier (Grenoble) – reference: L. Schwartz, Produits tensoriels topologiques d'espaces vectoriels topologiques, Applications, Séminaire Schwartz 1953–1954 – reference: H. Alexander, Analytic functions on Banach spaces, PhD thesis, University of California, Berkeley, 1968 – volume: 21 start-page: 7 year: 1976 end-page: 30 ident: bib005 article-title: Compact holomorphic mappings on Banach spaces and the approximation property publication-title: J. Funct. Anal. – year: 1981 ident: bib019 article-title: Locally Convex Spaces – volume: 7 start-page: 1 year: 1957 end-page: 141 ident: bib031 article-title: Théorie des distributions a valeurs vectoriells publication-title: Ann. Inst. Fourier (Grenoble) – year: 1999 ident: bib012 article-title: Complex Analysis on Infinite Dimensional Spaces – volume: 122 start-page: 139 year: 1997 end-page: 151 ident: bib022 article-title: Spaces of holomorphic functions on Banach spaces with a Schauder basis publication-title: Studia Math. – volume: 5 start-page: 243 year: 1957 end-page: 246 ident: bib007 article-title: On the weak continuity of the polynomial functions defined on the space publication-title: Bull. Pol. Acad. Sci. – volume: 209 start-page: 99 year: 1974 end-page: 107 ident: bib006 article-title: Bemerkungen über die Approximationseigenschaft lokalkonvexer Funktionenräume publication-title: Math. Ann. – volume: 271 start-page: 596 year: 1970 end-page: 598 ident: bib026 article-title: Sur les espaces vectoriels topologiques d'applications continues publication-title: C. R. Math. Acad. Sci. Paris – volume: 52 start-page: 189 year: 1983 end-page: 204 ident: bib004 article-title: Weakly continuous mappings on Banach spaces publication-title: J. Funct. Anal. – volume: 16 year: 1955 ident: bib016 article-title: Produits tensoriels topologiques et espaces nucléaires publication-title: Mem. Amer. Math. Soc. – volume: 16 start-page: 173 year: 1957 end-page: 182 ident: bib027 article-title: A property of multilinear operations publication-title: Studia Math. – volume: 90 start-page: 407 year: 1984 end-page: 411 ident: bib001 article-title: A reflexive space of holomorphic functions in infinitely many variables publication-title: Proc. Amer. Math. Soc. – volume: 27 start-page: 1009 year: 1997 end-page: 1027 ident: bib003 publication-title: Rocky Mountain J. Math. – volume: 328 start-page: 984 year: 2007 end-page: 994 ident: bib034 article-title: Polynomial approximation in Banach spaces publication-title: J. Math. Anal. Appl. – volume: vol. 120 year: 1986 ident: bib021 article-title: Complex Analysis in Banach Spaces publication-title: North-Holland Math. Stud. – volume: 8 start-page: 138 year: 1974 end-page: 141 ident: bib033 article-title: Not every Banach space contains an imbedding of publication-title: Funct. Anal. Appl. – volume: 126 start-page: 141 year: 2004 end-page: 156 ident: bib013 article-title: The approximation property for spaces of holomorphic functions on infinite dimensional spaces I publication-title: J. Approx. Theory – volume: 17 start-page: 153 year: 1997 end-page: 188 ident: bib014 article-title: Natural norms on symmetric tensor products of normed spaces publication-title: Note Mat. – reference: , in press – volume: vol. 1 year: 2009 ident: bib023 article-title: Spaces of Holomorphic Functions and the Approximation Property publication-title: IMI Graduate Lecture Notes – year: 1977 ident: bib020 article-title: Classical Banach Spaces I – reference: R. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, Doctoral thesis, Trinity College Dublin, 1980 – volume: 274 start-page: 1296 year: 1972 end-page: 1299 ident: bib017 article-title: Le problème de Levi dans les espaces de Banach à base publication-title: C. R. Math. Acad. Sci. Paris – volume: 22 start-page: 255 year: 1972 end-page: 292 ident: bib018 article-title: Prolongement analytique en dimension infinie publication-title: Ann. Inst. Fourier (Grenoble) – volume: 196 start-page: 106 year: 1972 end-page: 116 ident: bib011 article-title: Holomorphic functions on publication-title: Math. Ann. – volume: 29 start-page: 366 year: 1967 end-page: 368 ident: bib025 article-title: On the topology of the space of all holomorphic functions on a given open subset publication-title: Indag. Math. – year: 1960 ident: bib015 article-title: Rings of Continuous Functions – volume: 122 start-page: 139 year: 1997 ident: 10.1016/j.jfa.2010.04.001_bib022 article-title: Spaces of holomorphic functions on Banach spaces with a Schauder basis publication-title: Studia Math. doi: 10.4064/sm-122-2-139-151 – volume: 22 start-page: 255 issue: 2 year: 1972 ident: 10.1016/j.jfa.2010.04.001_bib018 article-title: Prolongement analytique en dimension infinie publication-title: Ann. Inst. Fourier (Grenoble) doi: 10.5802/aif.419 – volume: 328 start-page: 984 year: 2007 ident: 10.1016/j.jfa.2010.04.001_bib034 article-title: Polynomial approximation in Banach spaces publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.05.076 – year: 1977 ident: 10.1016/j.jfa.2010.04.001_bib020 – ident: 10.1016/j.jfa.2010.04.001_bib024 doi: 10.1007/s13163-009-0026-7 – volume: 17 start-page: 153 year: 1997 ident: 10.1016/j.jfa.2010.04.001_bib014 article-title: Natural norms on symmetric tensor products of normed spaces publication-title: Note Mat. – ident: 10.1016/j.jfa.2010.04.001_bib028 – volume: 196 start-page: 106 year: 1972 ident: 10.1016/j.jfa.2010.04.001_bib011 article-title: Holomorphic functions on (c0,Xb)-modules publication-title: Math. Ann. doi: 10.1007/BF01419608 – year: 1999 ident: 10.1016/j.jfa.2010.04.001_bib012 – volume: 126 start-page: 141 year: 2004 ident: 10.1016/j.jfa.2010.04.001_bib013 article-title: The approximation property for spaces of holomorphic functions on infinite dimensional spaces I publication-title: J. Approx. Theory doi: 10.1016/j.jat.2004.01.008 – ident: 10.1016/j.jfa.2010.04.001_bib030 – volume: 29 start-page: 366 year: 1967 ident: 10.1016/j.jfa.2010.04.001_bib025 article-title: On the topology of the space of all holomorphic functions on a given open subset publication-title: Indag. Math. doi: 10.1016/S1385-7258(67)50051-3 – volume: 5 start-page: 243 year: 1957 ident: 10.1016/j.jfa.2010.04.001_bib007 article-title: On the weak continuity of the polynomial functions defined on the space c0 publication-title: Bull. Pol. Acad. Sci. – volume: vol. 120 year: 1986 ident: 10.1016/j.jfa.2010.04.001_bib021 article-title: Complex Analysis in Banach Spaces – volume: 7 start-page: 1 year: 1957 ident: 10.1016/j.jfa.2010.04.001_bib031 article-title: Théorie des distributions a valeurs vectoriells publication-title: Ann. Inst. Fourier (Grenoble) doi: 10.5802/aif.68 – volume: 21 start-page: 7 year: 1976 ident: 10.1016/j.jfa.2010.04.001_bib005 article-title: Compact holomorphic mappings on Banach spaces and the approximation property publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(76)90026-4 – volume: 209 start-page: 99 year: 1974 ident: 10.1016/j.jfa.2010.04.001_bib006 article-title: Bemerkungen über die Approximationseigenschaft lokalkonvexer Funktionenräume publication-title: Math. Ann. doi: 10.1007/BF01351314 – volume: 12 start-page: 147 year: 2001 ident: 10.1016/j.jfa.2010.04.001_bib008 article-title: Weakly uniformly continuous holomorphic functions and the approximation property publication-title: Indag. Math. (N.S.) doi: 10.1016/S0019-3577(01)80022-7 – volume: vol. 1 year: 2009 ident: 10.1016/j.jfa.2010.04.001_bib023 article-title: Spaces of Holomorphic Functions and the Approximation Property – volume: 52 start-page: 189 year: 1983 ident: 10.1016/j.jfa.2010.04.001_bib004 article-title: Weakly continuous mappings on Banach spaces publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(83)90081-2 – volume: 8 start-page: 138 year: 1974 ident: 10.1016/j.jfa.2010.04.001_bib033 article-title: Not every Banach space contains an imbedding of ℓp or c0 publication-title: Funct. Anal. Appl. doi: 10.1007/BF01078599 – start-page: 261 year: 1975 ident: 10.1016/j.jfa.2010.04.001_bib029 article-title: ε-product and continuation of analytic mappings – volume: 16 year: 1955 ident: 10.1016/j.jfa.2010.04.001_bib016 article-title: Produits tensoriels topologiques et espaces nucléaires publication-title: Mem. Amer. Math. Soc. – volume: 90 start-page: 407 year: 1984 ident: 10.1016/j.jfa.2010.04.001_bib001 article-title: A reflexive space of holomorphic functions in infinitely many variables publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1984-0728358-5 – ident: 10.1016/j.jfa.2010.04.001_bib002 – volume: 271 start-page: 596 year: 1970 ident: 10.1016/j.jfa.2010.04.001_bib026 article-title: Sur les espaces vectoriels topologiques d'applications continues publication-title: C. R. Math. Acad. Sci. Paris – year: 1981 ident: 10.1016/j.jfa.2010.04.001_bib019 – volume: 16 start-page: 173 year: 1957 ident: 10.1016/j.jfa.2010.04.001_bib027 article-title: A property of multilinear operations publication-title: Studia Math. doi: 10.4064/sm-16-2-173-182 – volume: 36 start-page: 87 year: 1998 ident: 10.1016/j.jfa.2010.04.001_bib010 article-title: Polynomials on stable spaces publication-title: Ark. Mat. doi: 10.1007/BF02385668 – volume: 20 start-page: 361 issue: 1 year: 1970 ident: 10.1016/j.jfa.2010.04.001_bib009 article-title: Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'etude des fonctions analytiques publication-title: Ann. Inst. Fourier (Grenoble) doi: 10.5802/aif.345 – volume: 274 start-page: 1296 year: 1972 ident: 10.1016/j.jfa.2010.04.001_bib017 article-title: Le problème de Levi dans les espaces de Banach à base publication-title: C. R. Math. Acad. Sci. Paris – volume: 147 start-page: 89 year: 1981 ident: 10.1016/j.jfa.2010.04.001_bib032 article-title: B(H) does not have the approximation property publication-title: Acta Math. doi: 10.1007/BF02392870 – volume: 27 start-page: 1009 year: 1997 ident: 10.1016/j.jfa.2010.04.001_bib003 article-title: Q-reflexive Banach spaces publication-title: Rocky Mountain J. Math. doi: 10.1216/rmjm/1181071856 – year: 1960 ident: 10.1016/j.jfa.2010.04.001_bib015 |
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| Snippet | Let
H
(
U
)
denote the vector space of all complex-valued holomorphic functions on an open subset
U of a Banach space
E. Let
τ
ω
and
τ
δ
respectively denote... |
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| SubjectTerms | Banach space Holomorphic function Pseudoconvex Riemann domain Schauder basis |
| Title | The approximation property for spaces of holomorphic functions on infinite dimensional spaces II |
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