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d-ISOMETRIC LINEAR MAPPINGS IN LINEAR d-NORMED BANACH MODULES

Themistocles M. Rassias|박춘길
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 249-271

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참고문헌

키워드

Hyers–Ulam stabilitylinear d-normed Banach module over C*- algebraisometric isomorphismd-isometric isomorphismCauchy additive mapping
주제분류수학

초록

We prove the Hyers–Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital C*-algebra and of linear isometries in Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate d-isometric C*-algebra isomorphisms between linear d-normed C*-algebras and isometric C*-algebra isomorphisms between C*-algebras, and d-isometric Poisson C*-algebra isomorphisms between linear d-normed Poisson C*-algebras and isometric Poisson C*-algebra isomorphisms between Poisson C*-algebras. We moreover prove the Hyers–Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms.

Abstract

We prove the Hyers–Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital C*-algebra and of linear isometries in Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate d-isometric C*-algebra isomorphisms between linear d-normed C*-algebras and isometric C*-algebra isomorphisms between C*-algebras, and d-isometric Poisson C*-algebra isomorphisms between linear d-normed Poisson C*-algebras and isometric Poisson C*-algebra isomorphisms between Poisson C*-algebras. We moreover prove the Hyers–Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms.

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