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On Maximal Regular Ideals and Identities in the Tensor Product of Commutative Banach Algebras

Published online by Cambridge University Press:  20 November 2018

L. J. Lardy  and
J. A. Lindberg Jr.
L. J. Lardy
Affiliation:
Syracuse University, Syracuse, New York
J. A. Lindberg Jr.
Affiliation:
Syracuse University, Syracuse, New York
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Let A1 and A2 be commutative Banach algebras and A1 ⊙ A2 their algebraic tensor product over the complex numbers C.There is always a t least one norm, namely the greatest cross-norm γ (2), on A1 ⊙ A2 that renders it a normed algebra. We shall write A 1 ⊗αA2 for the α-completion of A1 ⊙ A2 when αis an algebra norm on A1 ⊙ A2.Gelbaum (2; 3), Tomiyama (9), and Gil de Lamadrid (4) have shown that for certain algebra norms α on A1 ⊙ A2 every complex homomorphism on A1 ⊙ A2 is α-continuous. In § 3 of this paper, we present a condition on an algebra norm α which is equivalent to the α-continuity of every complex homomorphism on A1 ⊙ A2.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 639 - 647
Copyright
Copyright © Canadian Mathematical Society 1969

References

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