Conditional weak compactness in vectorvalued function spaces
Author:
Marian Nowak
Journal:
Proc. Amer. Math. Soc. 129 (2001), 29472953
MSC (2000):
Primary 46B25, 46E40
Published electronically:
April 17, 2001
MathSciNet review:
1840098
Fulltext PDF Free Access
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Abstract: Let be an ideal of over a finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is bounded the following statement is equivalent to conditional compactness: the set is conditionally compact and is a conditionally weakly compact subset of for each , with . Applications to OrliczBochner spaces are given.
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Additional Information
Marian Nowak
Affiliation:
Institute of Mathematics, T. Kotarbiński Pedagogical University, Pl. Słowiański 9, 65–069 Zielona Góra, Poland
Email:
mnowa@lord.wsp.zgora.pl
DOI:
http://dx.doi.org/10.1090/S0002993901060646
PII:
S 00029939(01)060646
Keywords:
Conditional weak compactness,
vector valued function spaces
Received by editor(s):
July 6, 1998
Received by editor(s) in revised form:
February 14, 2000
Published electronically:
April 17, 2001
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2001
American Mathematical Society
