On a generalized trif's mapping in Banach modules over a c*-algebra

Park, C-G; Rassias, TM

dc.contributor.author	Park, C-G	en
dc.contributor.author	Rassias, TM	en
dc.date.accessioned	2014-03-01T01:24:46Z
dc.date.available	2014-03-01T01:24:46Z
dc.date.issued	2006	en
dc.identifier.issn	0304-9914	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17425
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-33644804175&partnerID=40&md5=05bdaa1a312c8de627c3d6aafc213b08	en
dc.subject	C*-algebra homomorphism	en
dc.subject	Cauchy-Rassias stability	en
dc.subject	Lie JC*-algebra derivation	en
dc.subject	Lie JC*-algebra homomorphisrn	en
dc.subject	Trif's functional equation	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	ULAM-RASSIAS STABILITY	en
dc.subject.other	FUNCTIONAL-EQUATION	en
dc.subject.other	JENSENS EQUATION	en
dc.subject.other	SPACES	en
dc.title	On a generalized trif's mapping in Banach modules over a c*-algebra	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	Let X and Y be vector spaces. It is shown that a mapping f : X --> Y satisfies the functional equation [GRAPHICS] if and only if the mapping f : X --> Y is additive, and we prove the Cauchy-Rassias stability of the functional equation (double dagger) in Banach modules over a unital C-algebra. Let A and B be unital C-algebras or Lie JC-algebras. As an application, we show that every almost homomorphism h: A --> B of A into B is a homomorphism when h(2(d)uy) = h(2(d)u)h(y) or h(2(d)u circle y) = h(2(d)u) circle h(y) for all unitaries u is an element of A, all y is an element of A, and d = 0, 1, 2,..., and that every almost linear almost multiplicative mapping h : A --> B is a homornorphism when h(2x) = 2h(x) for all x is an element of A. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in C-algebras or in Lie JC-algebras, and of Lie JC-algebra derivations in Lie JC*-algebras.	en
heal.publisher	KOREAN MATHEMATICAL SOCIETY	en
heal.journalName	Journal of the Korean Mathematical Society	en
dc.identifier.isi	ISI:000235770200008	en
dc.identifier.volume	43	en
dc.identifier.issue	2	en
dc.identifier.spage	323	en
dc.identifier.epage	356	en