In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of SchurCarathéodory, Nevanlinna-Pick, and Sarason type on Fock s...

We give a characterization of dynamical C*-systems such that the relative commutant of the fixed-point C*-algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point C*-algebra), in terms of suitable C*-algebra bundles. The group acting on the C*-algebra is the (noncompact, in general) space of sections of a compact group bundle. AMS Subj. C...

In the context of N. Brown’s Hom(N,RU ), we establish that given π : N → RU , the dimension of the minimal face containing [π] is one less than the dimension of the center of the relative commutant of π. We also show the “convex independence”of extreme points in the sense that the convex hull of n extreme points is an n-vertex simplex. Along the way, we establish a version of Schur’s Lemma for ...

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...

We give a characterization of C(X)-dynamical systems (B, G) such that the relative commutant of the fixed point algebra A := B is minimal (i.e. A′ ∩ B = (A∩A′)∨ (B ∩B′)) in terms of a field of C*-algebras over a suitable coset bundle. Here G is intended as the space of sections of a compact group bundle over X , so that it is a compact group when X is a single point. AMS Subj. Class.: 46L05, 55...

We study a W -algebra of central charge 2(k − 1)/(k + 2), k = 2, 3, . . . contained in the commutant of a Heisenberg algebra in a simple affine vertex operator algebra L(k, 0) of type A (1) 1 with level k. We calculate the operator product expansions of the W -algebra. We also calculate some singular vectors in the case k ≤ 6 and determine the irreducible modules and Zhu’s algebra. Furthermore,...

The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl2 on (C(q) ). We define and study a quotient of the BirmanWenzl-Murakami algebra, which plays an analogous role for the 3-dimensional representation of quantum sl2. In the course of the discussion we prove some general results about ...

Abstract We prove a double commutant theorem for separable subalgebras of wide class corona C * -algebras, largely resolving problem posed by Pedersen in 1988. Double theorems originated with von Neumann, whose seminal result evolved into an entire field now called Neumann algebra theory. Voiculescu later proved -algebraic the Calkin algebra. similar much more general so-called -algebras.