Isomorphisms in quasi-Banach algebras
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 111-118
Published online March 1, 2008
Choonkil Park and Jong Su An
Hanyang University and Pusan National University
Abstract : Using the Hyers--Ulam--Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy--Jensen functional equation $$2f(\frac{x+y}{2}+z) = f(x)+f(y)+2f(z),$$ which was introduced and investigated in [2, 17]. The concept of Hyers--Ulam--Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. $\bf 72$ (1978), 297--300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.
Keywords : Cauchy--Jensen functional equation, isomorphism, isometry, derivation, quasi-Banach algebra
MSC numbers : Primary 46B03, 47Jxx, 47B48
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