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http://dx.doi.org/10.4134/JKMS.2008.45.1.249

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

Park, Choon-Kil (Department of Mathematics Hanyang University)
Rassias, Themistocles M. (Department of Mathematics National Technical University of Athens Zogafou Campus)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 249-271 More about this Journal
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 $C^*-algebra$ 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.
Keywords
Hyers-Ulam stability; linear d-normed Banach module over $C^*-algebra$; isometric isomorphism; d-isometric isomorphism; Cauchy additive mapping;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
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