Annals of Functional Analysis

A fixed point approach to the stability of $\varphi$-morphisms on Hilbert $C^*$-modules

Gh. Abbaspour Tabadkan and M. Ramezanpour

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Let $E$, $F$ be two Hilbert $C^*$-modules over $C^*$-algebras $A$ and $B$ respectively. In this paper, by the alternative fixed point theorem, we give the Hyers-Ulam-Rassias stability of the equation $$\ip{U(x), U(y)}=\varphi( \ip{x,y})\qquad(x, y\in E),$$ where $U : E\to F$ is a mapping and $\varphi : A\to B$ is an additive map

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Ann. Funct. Anal., Volume 1, Number 1 (2010), 44- 50.

First available in Project Euclid: 12 May 2014

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Zentralblatt MATH identifier

Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 46L08: $C^*$-modules

Hyers-Ulam-Rassias stability Hilbert $C^*$-modules


Abbaspour Tabadkan, Gh.; Ramezanpour, M. A fixed point approach to the stability of $\varphi$-morphisms on Hilbert $C^*$-modules. Ann. Funct. Anal. 1 (2010), no. 1, 44-- 50. doi:10.15352/afa/1399900992.

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