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February 2019 I-convexity and Q-convexity in Orlicz–Bochner function spaces equipped with the Luxemburg norm
Wanzhong Gong, Xiaoli Dong, Kangji Wang
Ann. Funct. Anal. 10(1): 81-96 (February 2019). DOI: 10.1215/20088752-2018-0010

Abstract

We study I-convexity and Q-convexity, two geometric properties introduced by Amir and Franchetti. We point out that a Banach space X has the weak fixed-point property when X is I-convex (or Q-convex) with a strongly bimonotone basis. By means of some characterizations of I-convexity and Q-convexity in Banach spaces, we obtain criteria for these two convexities in the Orlicz–Bochner function space L(M)(μ,X): that L(M)(μ,X) is I-convex (or Q-convex) if and only if L(M)(μ) is reflexive and X is I-convex (or Q-convex).

Citation

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Wanzhong Gong. Xiaoli Dong. Kangji Wang. "I-convexity and Q-convexity in Orlicz–Bochner function spaces equipped with the Luxemburg norm." Ann. Funct. Anal. 10 (1) 81 - 96, February 2019. https://doi.org/10.1215/20088752-2018-0010

Information

Received: 10 February 2018; Accepted: 30 April 2018; Published: February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07045487
MathSciNet: MR3899958
Digital Object Identifier: 10.1215/20088752-2018-0010

Subjects:
Primary: 46B20
Secondary: 46E30

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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