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Tensor Products of Banach Algebras*

Published online by Cambridge University Press:  20 November 2018

Boaz Natzitz
Boaz Natzitz*
Affiliation:
McGill University
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In [3] Gelbaum defined the tensor product A ⊗CB of three commutative Banach algebras, A, B and C and established some of its properties. Various examples are given and the particular case where A, B and C are group algebras of L.C.A. groups G, H and K respectively, is discussed there. It is shown there that if K is compact L1(G) ⊗ L1(K) L1(H) is isomorphic to where is L.C.A. 1 L (K) 1 1 if and only if L1(G) ⊗ L1(K) L1(H) is semisimple.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 5 , December 1968 , pp. 691 - 701
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

**

The author wishes to thank Professor B.R. Gelbaum for his advice and encouragement.

*

Supported by Air Force Grant AFOSR-407-63, Yale University and N.S.F. Grant G. 24295, University of Minnesota.

References

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