Vol. 24, No. 2, 1968

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Group algebras of vector-valued functions

Donald Zane Spicer

Vol. 24 (1968), No. 2, 379–399

Let G be a compact group, 1 p < , and A be a Banach algebra. Define Bp(G,A) to be the set of all functions, f : G A, such that af(x)pdx < . Similarly define C(G,A) to be the set of all continuous functions from G to A. These sets form Banach algebras under the usual operations and convolution multiplication. This paper studies general properties of these algebras and in particular the inheritance of properties, such as structure, from the image algebra A. The techniques used, in part, involve certain topological tensor products, and the discussion is generalized to the context of more general topological tensor products.

Mathematical Subject Classification
Primary: 46.55
Received: 6 July 1966
Published: 1 February 1968
Donald Zane Spicer