We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

Let D ⊂ C be a bounded domain, whose boundary B consists of k simple closed continuous curves and H(D) be the algebra of bounded analytic functions on D. We prove the matrix-valued corona theorem for matrices with entries in H(D).

The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy–Foiaş theory, for row contractions. An n-tuple (T1, . . . , Tn) of operators acting on a Hilbert space is called row contraction if T1T ∗ 1 + · · ·+ TnT ∗ n ≤ I. In this study, the role of the unilateral shift is played by the left creation operators on the full Fock space ...

A C* algebra is a closed self-adjoint subalgebra of B(H), the bounded operators on a Hilbert space H. Kirchberg asked whether every C* algebra embeds into an ultrapower of a particular C* algebra, the Cuntz algebra O_2. In this talk, I will explain the model-theoretic content of this problem. In particular, I will show how model-theoretic forcing can be used to give a weak local reformulation o...

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that as...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

In this note we prove, for groups G fulfilling the Atiyah conjecture, a lemma relating arbitrary G-modules to free group-von-Neumann-algebra modules. As an immediate application we get properties of finitely generated pro-jective G-modules and G-modules. Other related arguments are envisaged. G; it can be defined as algebra of all (left) G-equivariant bounded linear operators on the Hilbert spa...

We study the following question in this paper: If p is a prime, m a positive integer, and S = (sm, . . . , s1) an arbitrary sequence consisting of “Y ”or “N”, does there exist a division algebra of exponent p over a valued field (F, v) such that the underlying division algebra of the tensor power D⊗p i has a valuation extending v if and only if sm−i = Y ? We show that if such an algebra exists,...

We construct a Banach space X of Gowers-Maurey type such that the algebra bounded operators L(X) is direct sum an infinite dimensional reflexive and operator ideal strictly singular SS(X).

A (distributive) p-algebra is an algebra 〈L;∨,∧, ∗, 0, 1〉 whose reduct 〈L;∨,∧, 0, 1〉 is a bounded (distributive) lattice and whose unary operation ∗ is characterized by x ≤ a if and only if a ∧ x = 0. If L is a p-algebra, B(L) = { x ∈ L : x = x } and D(L) = { x ∈ L : x = 1 } then 〈B(L);∪,∧, 0, 1〉 is a Boolean algebra when a ∪ b is defined to be (a∗ ∧ b∗)∗, for any a, b ∈ B(L), D∗(L) = { x ∨ x∗ ...