Products of group-valued measures
The investigation of the structure of biprojective Banach algebras with non-trivial radical [3] forces the author to suppose that the idea of projective cover, which is important in Ring Theory, can be effectively applied to Banach algebras and modules. But, in fact, the structural results on biprojectivity can be easier obtained without projective covers, so there are no references to this matter in [3]. Projective covers of Banach modules are considered in the present article. Except some assertions...
For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.