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APPROXIMATELY C*-INNER PRODUCT PRESERVING MAPPINGS

Mohammad Sal Moslehian|Jacek Chmielinski
대한수학회 (The Korean Mathematical Society)|2008.02|대한수학회보 (Bulletin of the KMS)|제45권 제1호|pp. 157-167

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참고문헌

키워드

Hyers–Ulam–Rassias stabilitysuperstabilityasymptotic behaviorHilbert C*-moduleorthogonality equation
주제분류수학

초록

A mapping f : M → N between Hilbert C-modules ap-proximately preserves the inner product if∥<f(x),f(y)> - <x,y>∥ ≤φ(x,y) for an appropriate control function φ(x,y) and all x,y ∈ M. In this pa-per, we extend some results concerning the stability of the orthogonalityequation to the framework of Hilbert C*-modules on more general re-stricted domains. In particular, we investigate some asymptotic behaviorand the HyersUlamRassias stability of the orthogonality equation.

Abstract

A mapping f : M → N between Hilbert C-modules ap-proximately preserves the inner product if∥<f(x),f(y)> - <x,y>∥ ≤φ(x,y) for an appropriate control function φ(x,y) and all x,y ∈ M. In this pa-per, we extend some results concerning the stability of the orthogonalityequation to the framework of Hilbert C*-modules on more general re-stricted domains. In particular, we investigate some asymptotic behaviorand the HyersUlamRassias stability of the orthogonality equation.

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