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Volume 27, Issue 4
Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach

M. Eshaghi Gordji, S. Kaboli Gharetapeh, M. Bidkham, T. Karimi & M. Aghaei

Anal. Theory Appl., 27 (2011), pp. 320-331.

Published online: 2011-11

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  • Abstract

Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A \to B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, \cdots$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.

  • AMS Subject Headings

39B82, 46HXX

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-27-320, author = {}, title = {Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {4}, pages = {320--331}, abstract = {

Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A \to B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, \cdots$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0320-3}, url = {http://global-sci.org/intro/article_detail/ata/4604.html} }
TY - JOUR T1 - Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach JO - Analysis in Theory and Applications VL - 4 SP - 320 EP - 331 PY - 2011 DA - 2011/11 SN - 27 DO - http://doi.org/10.1007/s10496-011-0320-3 UR - https://global-sci.org/intro/article_detail/ata/4604.html KW - alternative fixed point, Jordan $*$-homomorphism. AB -

Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A \to B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, \cdots$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.

M. Eshaghi Gordji, S. Kaboli Gharetapeh, M. Bidkham, T. Karimi & M. Aghaei. (1970). Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach. Analysis in Theory and Applications. 27 (4). 320-331. doi:10.1007/s10496-011-0320-3
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