We consider non-selfadjoint operator algebras L(G,λ) generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs G. These algebras may be viewed as noncommutative generalizations of weighted Bergman space algebras, or as weighted versions of the free semigroupoid algebras of directed graphs. A complete description of the commutant is obtained together with b...

The Hughston-Jozsa-Wootters (HJW) theorem entails that any finite ensemble compatible with a given density operator can be prepared from a fixed initial state by operations on a spacelike separated system. In this paper, we generalize the HJW theorem to the case of arbitrary measures on the state space of a von Neumann algebra with hyperfinite commutant. In doing so, we also show that every POV...

We study the commutant f(); 2

In this article we study and obtain a classification of Ising vectors in vertex operator algebras associated to binary codes and √ 2 times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating a simple Virasoro sub VOA. Then we apply our results to study certain commutant subalgebras related to root systems. We completely classify all Ising vectors in suc...

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the local commutant of a system. This is really an abstract application of the theory of operator algebras to wavelet theory. The concrete applications of this m...

This paper presents a few additions to commutant lifting theory. An operator interpolation problem is introduced and shown to be equivalent to the relaxed commutant lifting problem. Using this connection a description of all solutions of the former problem is given. Also a new application, involving bounded operators induced by H 2 operator-valued functions, is presented.

Abstract. In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting setting, and earlier obtained sufficient conditions turn out not to be necessary conditions. It is also shown that these conditions simplify in certain s...

Let T be the C∗-algebra generated by the Toeplitz operators {Tφ : φ ∈ L∞(S, dσ)} on the Hardy space H(S) of the unit sphere in C. It is well known that T is contained in the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)}. We show that the essential commutant of {Tφ : φ ∈ VMO∩L∞(S, dσ)} is strictly larger than T .

One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane C is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In [4], the first author obtained a complete description of the commutant of Toeplitz operator T with any quasihomogeneous symbol φ(...

Abstract We prove that a finite index regular inclusion of $II_1$ -factors with commutative first relative commutant is always crossed product subfactor respect to minimal action biconnected weak Kac algebra. Prior this, we every which depth 2 and has simple (respectively, or commutant) admits two-sided Pimsner–Popa basis unitary orthonormal basis).