$P$-convexity of Orlicz-Bochner spaces
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- by Paweł Kolwicz and Ryszard Płuciennik PDF
- Proc. Amer. Math. Soc. 126 (1998), 2315-2322 Request permission
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.References
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Additional Information
- Paweł Kolwicz
- Affiliation: Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland
- Email: kolwicz@math.put.poznan.pl
- Ryszard Płuciennik
- 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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2315-2322
- MSC (1991): Primary 46E30, 46E40, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-98-04290-7
- MathSciNet review: 1443391