ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS

doi:10.1016/S0252-9602(11)60231-2

Abstract

Abstract:

In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:
||f(x) + f(y) + 2f(z) + 2f(w)|| ≤||2f (x + y/2+ z + w) (0.1)
This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation
2f (x + y/2+ z + w )= f(x) + f(y) + 2f(z) + 2f(w). (0.2)

Key words: Jordan-von Neumann type Cauchy-Jensen functional equation, C*-algebra isomorphism, Lie C*-algebra isomorphism, JC*-algebra isomorphism, Hyers-Ulam-Rassias stability, Cauchy-Jensen functional inequality, deriva-tion

CLC Number:

39B52

Lee Jung-Rye, Shin Dong-Yun. ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS[J].Acta mathematica scientia,Series B, 2011, 31(1): 309-320.

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