Abstract
The algebraic tensor product A1⊗A2 of two Banach algebras is an algebra in a natural way. There are certain norms α on this tensor product for which the multiplication is continuous so that the completion, A1αA2, is a Banach algebra. The representation theory of such tensor products is the subject of this paper. It will be shown that, under certain simple conditions, the tensor product of two semi-simple Banach algebras is semi-simple although, without these conditions, the result fails.
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. The injective tensor product of ℒp-algebras
2. Resumé de la théorie métrique des produits tensoriels topologiques;Grothendieck;Bol. Soc. Mat,1956
3. Produits tensoriels topologiques et espaces nucléaires;Grothendieck;Mem. Amer. Math. Soc,1955
4. Banach Space Properties of Uniform Algebras†
5. Complete Normed Algebras
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