Let G denote a compact group
and B a homogeneous Banach space of pseudomeasures over G (B is left translation
invariant with continuous shifts). If T(G) is the linear space of trigonometric
polynomials defined on G then T(G) ∩ B is a dense subspace of B. An explicit
description is given of T(G) ∩ B. A complete list of the homogeneous closed
subspaces of B is given. Moreover it is shown that B is determined by the set
T(G) ∩B and N, the restriction of the B norm to this set. This leads to a complete
description of those subsets of T(G) and norms N which determine homogeneous
Banach spaces.
