文章基本信息

标题：Approximation of a generalized additive mapping in multi-Banach modules and isomorphisms in multi- C ∗ -algebras: a fixed-point approach
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作者：Choonkil Park ; Reza Saadati
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：162
DOI：10.1186/1687-1847-2012-162
语种：English
出版社：Hindawi Publishing Corporation
摘要：Let X , Y be vector spaces. It is shown that if an odd mapping f : X → Y satisfies the functional equation 0.1 then the odd mapping f : X → Y is additive, and we use a fixed-point method to prove the Hyers-Ulam stability of the functional equation (0.1) in multi-Banach modules over a unital multi- C ∗ -algebra. As an application, we show that every almost linear bijection h : A → B of a unital multi- C ∗ -algebra A onto a unital multi- C ∗ -algebra B is a C ∗ -algebra isomorphism when h ( 2 n r n u y ) = h ( 2 n r n u ) h ( y ) for all unitaries u ∈ U ( A ) , all y ∈ A , and n = 0 , 1 , 2 , … . MSC:39B52, 46L05, 47H10, 47B48.
关键词：C ∗ -algebra isomorphism ; fixed point ; generalized additive functional equation ; generalized Hyers-Ulam stability ; multi-Banach module over multi- C ∗ -algebra