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

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Park, Choon-Kil;Rassias, Themistocles M.

  • 발행 : 2008.01.31

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 $C^*-algebra$ isomor-phisms 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.

키워드

Hyers-Ulam stability;linear d-normed Banach module over $C^*-algebra$;isometric isomorphism;d-isometric isomorphism;Cauchy additive mapping

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