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ISSN 1449-5910  


Paper Information

Paper Title:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations


Javad Izadi and Bahmann Yousefi

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,



Let A be a Lie Banach*-algebra. For each elements (a, b) and (c, d) in A2:= A * A, by definitions

 (a, b) (c, d)= (ac, bd),
 |(a, b)|= |a|+ |b|,
(a, b)*= (a*, b*),

A2 can be considered as a Banach*-algebra. This Banach*-algebra is called a Lie Banach*-algebra whenever it is equipped with the following definitions of Lie product:

for all a, b, c, d in A. Also, if A is a Lie Banach*-algebra, then D: A2→A2 satisfying

 D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]

for all $a, b, c, d∈A, is a Lie derivation on A2. Furthermore, if A is a Lie Banach*-algebra, then D is called a Lie* derivation on A2 whenever D is a Lie derivation with D (a, b)*= D (a*, b*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach*-algebra homomorphisms and Lie* derivations on the Banach*-algebra A2.

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