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AUTOMATIC CONTINUITY OF n-HOMOMORPHISMS BETWEEN TOPOLOGICAL ALGEBRAS

Published online by Cambridge University Press:  01 April 2011

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:AB between algebras A and B is called n-multiplicative if θ(a1a2an)=θ(a1) θ(a2)⋯θ(an) for all elements a1,a2,…,anA. 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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