ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER \(CQ^*\)-ALGEBRAS


Authors

CHOONKIL PARK - Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133--791, South Korea. DEOK-HOON BOO - Department of Mathematics, Chungnam National University, Daejeon 305--764, South Korea.


Abstract

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in proper \(CQ^*\)-algebras and of generalized derivations on proper \(CQ^*\)-algebras for the following Cauchy-Jensen additive mappings: \[f (\frac{ x + y + z}{ 2 }) + f (\frac{ x - y + z}{ 2}) = f(x) + f(z),\] \[f (\frac{ x + y + z}{ 2 }) - f (\frac{ x - y + z}{ 2}) = f(y),\] \[2f (\frac{ x + y + z}{ 2 }) = f(x)+f(y)+f(z),\] which were introduced and investigated in [3, 30]. This is applied to investigate isomorphisms in proper \(CQ^*\)-algebras.


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ISRP Style

CHOONKIL PARK, DEOK-HOON BOO, ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER \(CQ^*\)-ALGEBRAS, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 1, 19-36

AMA Style

PARK CHOONKIL, BOO DEOK-HOON, ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER \(CQ^*\)-ALGEBRAS. J. Nonlinear Sci. Appl. (2011); 4(1):19-36

Chicago/Turabian Style

PARK , CHOONKIL, BOO, DEOK-HOON. "ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER \(CQ^*\)-ALGEBRAS." Journal of Nonlinear Sciences and Applications, 4, no. 1 (2011): 19-36


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