Abstract
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.
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