Geodesic
On Maximal Regular Ideals and Identities in the Tensor Product of Commutative Banach Algebras
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 639-647

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Lardy, L. J.; Jr., J. A. Lindberg. On Maximal Regular Ideals and Identities in the Tensor Product of Commutative Banach Algebras. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 639-647. doi: 10.4153/CJM-1969-072-3
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