Primitive Ideals in Tensor Products of Banach Algebras.
Problems concerning -weak amenability of a Banach algebra
In this paper we extend the notion of -weak amenability of a Banach algebra when . Technical calculations show that when is Arens regular or an ideal in , then is an -module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of -weak amenability to .
Projective covers of finitely generated Banach modules and the structure of some Banach algebras.
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...
Projective Hilbert A(D)-modules.
Projective limits of topological algebras
Projectivity and lifting of Hilbert module maps
In a recent paper, Carlson, Foiaş, Williams and the author proved that isometric Hilbert modules are projective in the category of Hilbert modules similar to contractive ones. In this paper, a simple proof, based on a strengthened lifting theorem, is given. The proof also applies to an equivalent theorem of Foiaş and Williams on similarity to a contraction of a certain 2 × 2 operator matrix.
Properties of derivations on some convolution algebras
For all convolution algebras L 1[0, 1); L loc1 and A(ω) = ∩n L 1(ωn), the derivations are of the form D μ f = Xf * μ for suitable measures μ, where (Xf)(t) = tf(t). We describe the (weakly) compact as well as the (weakly) Montel derivations on these algebras in terms of properties of the measure μ. Moreover, for all these algebras we show that the extension of D μ to a natural dual space is weak-star continuous.
Properties of the spectral radius in Banach algebras
Propriétés analytiques du spèctre dans les algèbres de Jordan-Banach.
Propriétés multiplicatives universelles de certains quotients d'algèbres de Fréchet
Propriétés spectrales en analyse non archimédienne
Pseudo-amenability of Brandt semigroup algebras
In this paper it is shown that for a Brandt semigroup over a group with an arbitrary index set , if is amenable, then the Banach semigroup algebra is pseudo-amenable.
Pseudo-Banach algebras
Pseudo-inverses, holomorphic functions and Atkinson theory in Banach algebras.
Pure states on Jordan algebras
We prove that a pure state on a -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute...