On a class of linear operators.
On Arens-Michael algebras which do not have non-zero injective ⨶-modules
A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in , algebras of smooth functions on domains in , algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.
On barrelled topological modules.
On character amenable Banach algebras
We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...
On (Co)homology of triangular Banach algebras
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.
On differences of Riesz homomorphisms.
On holomorphy in Banach spaces and absolute convergence of Fourier series
On modules of continuous linear mappings.
On quadratic and sesquilinear functionals.
On relative amenability for von Neumann algebras
On Tensor Products of Banach Lattices.
On the Cauchy functional inequality in Banach modules.
On the closure of modules of continuously differentiable mappings
On the projectivity and flatness of some group modules
In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.
On the structure of derivations on certain nonamenable nuclear Banach algebras.
On the weak amenability of ℬ(X)
We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.
On topological modules and duality
On unitary equivalence of quasi-free Hilbert modules
We characterize unitary equivalence of quasi-free Hilbert modules, which complements Douglas and Misra's earlier work [New York J. Math. 11 (2005)]. We first confine our arguments to the classical setting of reproducing Hilbert spaces and then relate our result to equivalence of Hermitian vector bundles.
Operators which respect norm intervals