We develop a theory of holomorphic functions in several noncommuting (free) variables and
provide a framework for the study of tuples of bounded linear operators on Hilbert spaces …

Subproduct Systems Page 1 Documenta Math. 801 Subproduct Systems Orr Moshe Shalit and
Baruch Solel 1 Received: July 1, 2009 Revised: August 12, 2009 Communicated by Joachim …

We develop a dilation theory on noncommutative varieties determined by row contractions
T:= T1,..., Tn subject to constraints such as p (T1,..., Tn)= 0, p∈ P, where P is a set of …

In this volume we study noncommutative domains $\mathcal {D} _f\subset B (\mathcal {H})^
n $ generated by positive regular free holomorphic functions $ f $ on $ B (\mathcal {H})^ n …

In this paper we study the operator inequality j Xfi e X and the operator equation j Xfi º X,
where j is aw√-continuous positive (resp. completely positive) linear map on B Hfi. We …

A celebrated theorem of Pimsner states that a covariant representation T of a C*-
correspondence E extends to a C*-representation of the Toeplitz algebra of E if and only if T …

In this paper, we study free pluriharmonic functions on noncommutative balls [Formula: see
text], γ> 0, and their boundary behavior. These functions have the form where the …

In this paper we obtain a noncommutative multivariable analogue of the classical
Nevanlinna–Pick interpolation problem for analytic functions with positive real parts on the …

For commuting contractions $ T_1,\dots, T_n $ acting on a Hilbert space $\mathcal H $ with
$ T=\prod_ {i= 1}^ n T_i $, we find a necessary and sufficient condition under which …

Here we study dilations of q-commuting tuples. In [BBD] the authors gave the
correspondence between the two standard dilations of commuting tuples and here these …