相关论文: Diagonals in Tensor Products of Operator Algebras

We investigate the higher-dimensional amenability of tensor products $\A \ptp \B$ of Banach algebras $\A$ and $\B$. We prove that the weak bidimension $db_w$ of the tensor product $\A \ptp \B$ of Banach algebras $\A$ and $\B$ with bounded…

Let $X$ be an operator space, let $\phi$ be a product on $X$, and let $(X,\phi)$ denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping $\phi$ for the algebra $(X,\phi)$ to have a completely…

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of…

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…

A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…

The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…

We study the relation between module and Hochschild cohomology groups of Banach algebras with a compatible module structure. More precisely, we show that for every commutative Banach $ \mathcal{A} $-$ \mathfrak{A}$-bimodule $ X $ and every…

It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can exist. In particular,…

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types of algebras with the aim of providing an inductive step towards the proof of this conjecture. Firstly we show that if an algebra…

Let $A$ be a unital Banach algebra. We give a characterization of the left Banach $A$-modules $X$ for which there exists a commutative unital $C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive unital homomorphism…

We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with…

Given a central arrangement of lines $\mathcal{A}$ in a $2$-dimensional vector space $V$ over a field of characteristic zero, we study the algebra $\mathcal D(\mathcal A)$ of differential operators on $V$ which are logarithmic along…

Let $\cal A$ be a Banach algebra. We study those closed ideals $I$ of $\cal A$ for which the first cohomology group of $\cal A$ with coefficients in $I^*$ is trivial; i.e. $H^1(\cal A,I^*)=\{0\}$. We investigate such closed ideals when…

To a given multivariable C*-dynamical system $(A, \al)$ consisting of *-automorphisms, we associate a family of operator algebras $\alg(A, \al)$, which includes as specific examples the tensor algebra and the semicrossed product. It is…

A Banach space operator $T\in B(X)$ is left polaroid if for each $\lambda\in\hbox{iso}\sigma_a(T)$ there is an integer $d(\lambda)$ such that asc $(T-\lambda)=d(\lambda)<\infty$ and $(T-\lambda)^{d(\lambda)+1}X$ is closed; $T$ is finitely…

It is established in this work that second Hochshild cohomology group of the associative conformal algebra Cend_{1,x} is zero. As a corollary, this algebra split off in each extension with a nilpotent kernel. Key words: associative…

We give an explicit description of a diagonal map on the Bardzell resolution for any monomial algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is zero in…

We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator…

A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly…

This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…