Gudder–Nagy’s Theorem for Hilbert K(H)-Modules

Ming-Hsiu Hsu

Journal of Mathematics, 2025, vol. 2025, 1-4

Abstract: We show in this paper Gudder–Nagy’s theorem for operators on Hilbert C∗-modules over C∗-algebra of compact operators. Let H be a complex Hilbert space with dim H>1, and KH the C∗-algebra of compact operators on H. For bounded KH-linear operators A,B and C on Hilbert C∗-module X over KH, we show that Ax,xBx,x=x,xCx,x, for all x∈X, if and only if there is a complex number λ such that A=λI and C=λB.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3623110

DOI: 10.1155/jom/3623110

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