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2010•Korean Journal of MathematicsRequires access

ALMOST HOMOMORPHISMS BETWEEN BANACH ALGEBRAS

Sung Jin Lee, Choonkil Park

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Abstract

It is shown that for an almost algebra homomorphism between Banach algebras, there exists a unique algebra homomorphism near the almost algebra homomorphism. Moreover, we prove that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism, and that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism.

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What this paper is about

It is shown that for an almost algebra homomorphism between Banach algebras, there exists a unique algebra homomorphism near the almost algebra homomorphism. Moreover, we prove that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism, and that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism.

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Available abstract

It is shown that for an almost algebra homomorphism between Banach algebras, there exists a unique algebra homomorphism near the almost algebra homomorphism. Moreover, we prove that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism, and that for an almost algebra *-homomorphism between -algebras, there exists a unique algebra *-homomorphism near the almost algebra *-homomorphism.

Key concepts: Homomorphism, Algebra homomorphism, Mathematics, Banach algebra, Algebra over a field, Pure mathematics, Division algebra, Cellular algebra

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