Suppose that A and B are unital Banach algebras with units and , respectively, M is a unital Banach A,B-module, is the triangular Banach algebra, X is a unital -bimodule, , , and . Applying two nice long exact sequences related to A, B, , X, , , and we establish some results on (co)homology of triangular Banach algebras.
An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.
We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.
Let be a norm on the algebra of all matrices over . An interesting problem in matrix theory is that “Are there two norms and on such that for all ?” We will investigate this problem and its various aspects and will discuss some conditions under which .
A surjective bounded homomorphism fails to preserve -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
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