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On Automatic Continuity of 3-Homomorphisms on Banach Algebras

Bracic, Janko, and Moslehian, Mohammad Sal, (2007) On Automatic Continuity of 3-Homomorphisms on Banach Algebras. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 195-200. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v30n2/v30n2p10.pdf

Affiliations

University of Ljubljana, Dept. of Mathematics
Ferdowsi University, Dept. of Mathematics

Abstract

A linear map $\varphi : \mathcal{A} \rightarrow \mathcal{B}$ between (Banach) algebras is called 3- homomorphism if $\varphi (abc) = \varphi (a)\varphi (b)\varphi (c)$ for each $a, b, c \in \mathcal{A}$. We investigate 3-homomorphisms on Banach algebras with bounded approximate identities and establish in two ways (for unital and non-unital cases) that every involution preserving homomorphism between $C^\ast$-algebras is norm decreasing.

Item Type:Journal
Keywords:3-homomorphism, Homomorphism, Continuity, Banach algebra, Bounded approximate identity, Second dual, Arens regularity, C*-algebra.
Subjects:Q Science, Computer Science
ID Code:1459

[1] H.G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monographs 24, Clarendon Press, Oxford, 2000.

[2] L.A. Harris, A generalization of C*-algebras, Proc. Lond. Math. Soc. 42(3)(1981), 331-361.

[3] S. Hejazian, M. Mirzavaziri and M.S. Moslehian, n-homomorphisms, Bull. Iranian Math. Soc. 31(1)(2005), 13—23.

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