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

Author

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  • Kourosh Nourouzi

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.

Suggested Citation

  • Kourosh Nourouzi, 2026. "Reflexivity of Hilbert KH-Modules and Fixed-Point Property for Nonexpansive Mappings," Journal of Mathematics, Hindawi, vol. 2026, pages 1-5, September.
    • Handle: RePEc:hin:jjmath:6311273
    DOI: 10.1155/jom/6311273
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