APPROXIMATELY C*-INNER PRODUCT PRESERVING MAPPINGS

Title & Authors
APPROXIMATELY C*-INNER PRODUCT PRESERVING MAPPINGS

Abstract
A mapping f : $\small{M{\rightarrow}N}$ between Hilbert $\small{C^*}$-modules approximately preserves the inner product if $\small{\parallel}$<$\small{f(x),\;f(y)}$>$\small{-}$<$\small{x,y}$>$\small{\parallel\leq\varphi(x,y)}$ for an appropriate control function $\small{\varphi(x,y)}$ and all x, y $\small{\in}$ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert $\small{C^*}$-modules on more general restricted domains. In particular, we investigate some asymptotic behavior and the Hyers-Ulam-Rassias stability of the orthogonality equation.
Keywords
Hilbert $\small{C^*}$-module;Hyers-Ulam-Rassias stability;superstability;orthogonality equation;asymptotic behavior;
Language
English
Cited by
1.
Orthogonalities and functional equations, Aequationes mathematicae, 2015, 89, 2, 215
2.
Perturbation of the Wigner equation in inner product C*-modules, Journal of Mathematical Physics, 2008, 49, 3, 033519
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