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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| Vydáno v: | Journal of functional analysis Ročník 259; číslo 2; s. 545 - 560 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.07.2010
|
| Témata: | |
| ISSN: | 0022-1236, 1096-0783 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
|---|---|
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1016/j.jfa.2010.04.001 |