Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology
Let X be a completely regular Hausdorff space and let E , · E and ( F , · F ) be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology β σ . We study the relationship between important classes of ( β σ , · F ) -continuou...
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| Veröffentlicht in: | Journal of function spaces Jg. 2015; H. 2015; S. 1 - 13 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2015
John Wiley & Sons, Inc Wiley |
| Schlagworte: | |
| ISSN: | 2314-8896, 2314-8888 |
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| Abstract | Let X be a completely regular Hausdorff space and let E , · E and ( F , · F ) be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology β σ . We study the relationship between important classes of ( β σ , · F ) -continuous linear operators T : C b ( X , E ) →F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. |
|---|---|
| AbstractList | Let
X
be a completely regular Hausdorff space and let
E
,
·
E
and
(
F
,
·
F
)
be Banach spaces. Let
C
b
(
X
,
E
)
be the space of all
E
-valued bounded, continuous functions on
X
, equipped with the strict topology
β
σ
. We study the relationship between important classes of
(
β
σ
,
·
F
)
-continuous linear operators
T
:
C
b
(
X
,
E
)
→F
(strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Let X be a completely regular Hausdorff space and let ( E , [subscript] || · || E [/subscript] ) and ( F , [subscript] || · || F [/subscript] ) be Banach spaces. Let [subscript] C b [/subscript] ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology [subscript] β σ [/subscript] . We study the relationship between important classes of ( [subscript] β σ [/subscript] , [subscript] || · || F [/subscript] ) -continuous linear operators T : [subscript] C b [/subscript] ( X , E ) [arrow right]F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Let X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology βσ. We study the relationship between important classes of (βσ,·F)-continuous linear operators T:Cb(X,E)→F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Let X be a completely regular Hausdorff space and let E , · E and ( F , · F ) be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology β σ . We study the relationship between important classes of ( β σ , · F ) -continuous linear operators T : C b ( X , E ) →F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Let X be a completely regular Hausdorff space and let E, sub(.E) and (F, sub(.F) ) be Banach spaces. Let sub(Cb) (X,E) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology sub( beta sigma ) . We study the relationship between important classes of ( sub( beta sigma ) , sub(.F) ) -continuous linear operators T: sub(Cb) (X,E) arrow right F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. |
| Author | Nowak, Marian |
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| CitedBy_id | crossref_primary_10_1515_math_2016_0043 |
| Cites_doi | 10.4064/fm-60-1-1-22 10.4153/CJM-1953-017-4 10.1007/bf02416964 10.1016/0001-8708(78)90009-9 10.21136/CMJ.1971.101000 10.4064/sm-36-3-195-212 10.1002/mana.19891430125 10.1090/s0002-9947-1974-0338821-5 10.1006/jmaa.1995.1353 10.1007/BF01461727 10.1017/s0305004100062678 10.1016/0022-1236(69)90012-3 10.1017/s030500410006919x 10.1002/9781118033012 10.4153/CJM-1974-079-1 10.1216/rmjm/1181072710 10.4064/sm-17-2-151-164 10.2307/2046087 10.1090/S0002-9947-1975-0365111-8 10.1017/S0017089500008259 10.1016/j.jmaa.2011.10.033 10.2140/pjm.1974.53.207 10.1007/bf01202500 10.1017/S0305004100070584 10.1215/ijm/1255987796 10.1007/978-1-4612-5200-9 10.4064/sm-33-3-295-298 10.1017/S030500410006134X 10.2307/1998840 10.1007/bf02760458 10.21136/CMJ.1970.100979 10.1090/s0002-9947-1972-0295065-1 |
| ContentType | Journal Article |
| Copyright | Copyright © 2015 Marian Nowak. Copyright © 2015 Marian Nowak. Marian Nowak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Copyright_xml | – notice: Copyright © 2015 Marian Nowak. – notice: Copyright © 2015 Marian Nowak. Marian Nowak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2015/796753 |
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| Snippet | Let X be a completely regular Hausdorff space and let E , · E and ( F , · F ) be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded,... Let X be a completely regular Hausdorff space and let E , · E and ( F , · F ) be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded,... Let X be a completely regular Hausdorff space and let ( E , [subscript] || · || E [/subscript] ) and ( F , [subscript] || · || F [/subscript] ) be Banach... Let X be a completely regular Hausdorff space and let E, sub(.E) and (F, sub(.F) ) be Banach spaces. Let sub(Cb) (X,E) be the space of all E -valued bounded,... Let X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions... |
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| SubjectTerms | Banach space Function space Linear operators Operators Theorems Topology |
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| Title | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
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