Related papers: A Banach Algebra Approach To Amalgamated R- and S-…
We show that every R-diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu's…
In this article, we attempt to introduce the "Multiplier algebra" associated to the Fock representation that arising from the left-cancellative semigroup $\mathcal{S}$ (denoted by $M(\mathcal{S})$) by adopting the concept of multiplier…
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators,…
In the present paper we investigate Banach--Kantorovich algebras over faithful solid subalgebras of algebras measurable functions. We prove that any Banach--Kantorovich algebra over faithful solid subalgebras of algebra measurable functions…
In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a…
The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space geomtry.
It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if, G is exact and non-amenable. This construction allows a…
The fully matricial generalization in part I, of the difference quotient derivation on holomorphic functions, in which ${\mathbb C}$ is replaced by a Banach algebra $B$, is extended from the affine case to a Grassmannian completion. The…
We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We…
Let $\mathcal{L}$ be a completely distributive commutative subspace lattice or a subspace lattice with two atoms, we use a unified approach to study the derivations, homomorphisms on $\mathrm{Alg} \mathcal{L}$. We verify that the multiplier…
Let $X$ be a locally compact Hausdorff space, and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of BSE- Banach algebras $A$, and the Banach algebra $C_{0}(X, A)$…
We show that a unital involutive Banach algebra, with identity of norm one and continuous involution, is a C*-algebra, with the given involution and norm, if every continuous linear functional attaining its norm at the identity is positive.
We revisit the twisted multiplicativity property of Voiculescu's S-transform in the operator-valued setting, using a specific bijection between planar binary trees and noncrossing partitions.
A net $(x_\alpha)$ in an $f$-algebra $E$ is called multiplicative order convergent to $x\in E$ if $\lvert x_\alpha-x\rvert u\oc 0$ for all $u\in E_+$. This convergence has been investigated and applied in a recent paper by Ayd{\i}n…
Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(\alpha, \sigma)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on…
It has been shown by Voiculescu and Biane that the analytic subordination property holds for free additive and multiplicative convolutions. In this paper, we present an operatorial approach to subordination for free multiplicative…
An L-embedded Banach spaace is a Banach space which is complemented in its bidual such that the norm is additive between the two complementary parts. On such spaces we define a topology, called an abstract measure topology, which by known…
We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding…
Let A be a unital $C^*$-algebra, given together with a specified state $\phi:A \to C$. Consider two selfadjoint elements a,b of A, which are free with respect to $\phi$ (in the sense of the free probability theory of Voiculescu). Let us…