ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER $CQ^*$-ALGEBRAS

PARK , CHOONKIL ¹ ; BOO, DEOK-HOON²

¹ Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133--791, South Korea
² Department of Mathematics, Chungnam National University, Daejeon 305--764, South Korea

Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 1, p. 19-36.

Résumé

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.

Détail

DOI : 10.22436/jnsa.004.01.03

Classification : 39B72, 17A40, 46L05, 46B03, 47Jxx
Keywords: Hyers-Ulam-Rassias stability, Cauchy-Jensen functional equation, proper \(CQ^*\)-algebra isomorphism, generalized derivation.

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