Schur class operator functions and automorphisms of Hardy algebras.
Sectional Representation of Banach Modules.
Sectional representation of Banach modules and their multipliers.
Sesquilinear and Quadratic Forms on Modules Over *-algebras
Sheaves of metric lattices
Some extremal properties of section spaces of Banach bundles and their duals.
Some homological properties of Banach algebras associated with locally compact groups
We investigate some homological notions of Banach algebras. In particular, for a locally compact group G we characterize the most important properties of G in terms of some homological properties of certain Banach algebras related to this group. Finally, we use these results to study generalized biflatness and biprojectivity of certain products of Segal algebras on G.
Some module cohomological properties of Banach algebras
We find some relations between module biprojectivity and module biflatness of Banach algebras and and their projective tensor product . For some semigroups , we study module biprojectivity and module biflatness of semigroup algebras .
Some notions of amenability for certain products of Banach algebras
For two Banach algebras and ℬ, an interesting product , called the θ-Lau product, was recently introduced and studied for some nonzero characters θ on ℬ. Here, we characterize some notions of amenability as approximate amenability, essential amenability, n-weak amenability and cyclic amenability between and ℬ and their θ-Lau product.
Spaces of multipliers and their preduals for the order multiplication on [0, 1]
Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise and their preduals.
Spatiality of derivations of Fréchet GB*-algebras
We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
Spectral and homological properties of Hilbert modules over the disc algebra
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.
Spectral Decompositions and Decomposable Multipliers.
Spectral properties of quotients of Beurling-type submodules of the Hardy module over the unit ball
Let M be a Beurling-type submodule of , the Hardy space over the unit ball of , and let be the associated quotient module. We completely describe the spectrum and essential spectrum of N, and related index theory.
Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras
We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].
Stability of a 2-dimensional functional equation in a class of vector variable functions.
Structure theory of homologically trivial and annihilator locally C*-algebras
We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C*-algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C*-algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically...
Superstability for generalized module left derivations and generalized module derivations on a Banach module. II.