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AUTOMATIC CONTINUITY OF n-HOMOMORPHISMS BETWEEN TOPOLOGICAL ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  01 April 2011

TAHER G. HONARY  and
H. SHAYANPOUR
TAHER G. HONARY*
Affiliation:
Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, Tehran 1561836314, Iran (email: [email protected])
H. SHAYANPOUR
Affiliation:
Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, Tehran 1561836314, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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A map θ:A→B between algebras A and B is called n-multiplicative if θ(a1a2⋯an)=θ(a1) θ(a2)⋯θ(an) for all elements a1,a2,…,an∈A. If θ is also linear then it is called an n-homomorphism. This notion is an extension of a homomorphism. We obtain some results on automatic continuity of n-homomorphisms between certain topological algebras, as well as Banach algebras. The main results are extensions of Johnson’s theorem to surjective n-homomorphisms on topological algebras, a theorem due to C. E. Rickart in 1950 to dense range n-homomorphisms on topological algebras and two theorems due to E. Park and J. Trout in 2009 to * -preserving n-homomorphisms on lmc * -algebras.

Keywords

automatic continuityn-homomorphismtopological algebraslmc algebrasQ-algebrasn-involution*-preserving n-homomorphisms

MSC classification

Secondary: 46H40: Automatic continuity 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 389 - 400
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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