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 ∫a∥f(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.
