Reflexivity of Hilbert KH-Modules and Fixed-Point Property for Nonexpansive Mappings

Kourosh Nourouzi

Journal of Mathematics, 2026, vol. 2026, 1-5

Abstract: We prove that a Hilbert C∗-module over the C∗-algebra KH of all compact operators on a complex infinite dimensional Hilbert space H is reflexive as a Banach space if and only if its orthogonal dimension is finite. In particular, a Hilbert KH-module has the fixed-point property (FPP) for nonexpansive mappings if and only if it is reflexive as a Banach space. This classification result identifies a new class of reflexive Banach spaces, namely, KH-Hilbert modules of finite orthogonal dimension, that possess the FPP for nonexpansive mappings.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6311273

DOI: 10.1155/jom/6311273

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