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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$P$-convexity of Orlicz-Bochner spaces


Authors: Pawe\l{} Kolwicz and Ryszard Pluciennik
Journal: Proc. Amer. Math. Soc. 126 (1998), 2315-2322
MSC (1991): Primary 46E30, 46E40, 46B20
MathSciNet review: 1443391
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Abstract: A characterization of $P$-convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space $L$ $_\Phi (\mu ,X)$ is P-convex if and only if both spaces $L_\Phi (\mu )$ and $X$ are $P$-convex. In particular, the Lebesgue-Bochner space $L^p(\mu ,X)$ with $1<p<\infty $ is $P$-convex iff $X$ is $P$-convex.


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Additional Information

Pawe\l{} Kolwicz
Affiliation: Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland
Email: kolwicz@math.put.poznan.pl

Ryszard Pluciennik
Affiliation: Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland
Email: rplucien@piglet.wsb.poznan.pl, rplucien@math.put.poznan.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04290-7
PII: S 0002-9939(98)04290-7
Keywords: Orlicz-Bochner space, $P$-convexity, Orlicz space
Received by editor(s): February 14, 1996
Received by editor(s) in revised form: January 13, 1997
Additional Notes: The first author was supported by the Foundation for Polish Science-scholarship ’97
The second author was supported by KBN grant 2 PO3A 031 10
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society