ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER \(CQ^*\)-ALGEBRAS
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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.
Share and Cite
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
Keywords
- Hyers-Ulam-Rassias stability
- Cauchy-Jensen functional equation
- proper \(CQ^*\)-algebra isomorphism
- generalized derivation.
MSC
- 39B72
- 17A40
- 46L05
- 46B03
- 47Jxx
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