Related papers: Stable isomorphisms of operator algebras

We study operator algebraic and function theoretic aspects of algebras of bounded nc functions on subvarieties of the nc domain determined by all levels of the unit ball of an operator space (nc operator balls). Our main result is the…

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…

We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and…

An implicit operation of a class of similar algebras $\mathsf{K}$ is a collection of first order definable partial functions on the members of $\mathsf{K}$ that is globally preserved by homomorphisms. For instance, "taking inverses" can be…

The notion of isomorphism of stable AF-C*-algebras is considered in this paper in the case when the corresponding Bratteli diagram is stationary, i.e., is associated with a single square primitive nonsingular incidence matrix.…

We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential operators introduced by Grunbaum and Yakimov…

We study differential graded operads and $p$-adic stable homotopy theory. We first construct a new class of differential graded operads, which we call the stable operads. These operads are, in a particular sense, stabilizations of…

Let $E = (E^0, E^1, r, s)$ be a topological graph with no sinks such that $E^0$ and $E^1$ are compact. We show that when $C^*(E)$ is finite, there is a natural isomorphism $C^*(E) \cong C(E^\infty) \rtimes \mathbb{Z}$, where $E^\infty$ is…

We show that the K_1 group of a C*-algebra $A$ can be defined as homotopy classes of pairs, called balanced, of not necessarily unitary matrices over $A$ that have equal defects from being unitary. We also consider pairs of order zero…

Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category O of the Borel subalgebra of an arbitrary untwisted quantum affine…

We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse…

We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…

We study stable subspaces of positive extremal maps of finite dimensional matrix algebras that preserve trace and matrix identity (so-called bistochastic maps). We have established the existence of the isometric-sweeping decomposition for…

A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither…

A profinite group is index-stable if any two isomorphic open subgroups have the same index. Let $p$ be a prime, and let $G$ be a compact $p$-adic analytic group with associated $\mathbb{Q}_p$-Lie algebra $\mathcal{L}(G)$. We prove that $G$…

Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a $C^\star$-algebra onto a Banach algebra. We then use this result to show that a $C^\star$-algebra $A$ is isomorphic to a…

We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show…

It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…

Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for $G$ and the…