Related papers: Isometric dilation and Sarason's commutant lifting…

The theorem on the existence of three commuting contractions on a Hilbert space and of a linear homogeneous matrix function of three independent variables for which the generalized von Neumann inequality fails is proved.

We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…

A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling…

We introduce the notion of $*$-regular dilation for q-commuting tuples of contractions and generalize the results due to Gaspar-Suciu and Timotin on commuting contractions.

The fundamental result of B. Sz. Nazy states that every contraction has a coisometric extension and a unitary dilation. The isometric dilation of a contraction on a Hilbert space motivated whether this theory can be extended sensibly to…

Suppose that $n\geq 1$ and that, for all $i$ and $j$ with $1\leq i,j\leq n$ and $i\neq j$, $z_{ij}\in{\mathbb T}$ are given such that $z_{ji}=\overline{z}_{ij}$ for all $i\neq j$. If $V_1,\dotsc, V_n$ are isometries on a Hilbert space such…

In this paper, we obtain a complete description of the class of n-tuples (n >= 2) of doubly commuting isometries. In particular, we present a several variables analogue of the Wold decomposition for isometries on Hilbert spaces. Our main…

A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.

For a tuple $T$ of Hilbert space operators, the 'commuting dilation constant' is the smallest number $c$ such that the operators of $T$ are a simultaneous compression of commuting normal operators of norm at most $c$. We present numerical…

Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commuting $n$-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough to determine if an $n$-tuple is free. In…

We obtain dilation results which simultaneously generalize Sz.-Nagy dilation theorem for contractions, Ando's dilation theorem for commuting contractions, Sz.-Nagy--Foias commutant lifting theorem, and Schur's representation for the unit…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the row operator $(V_1,...,V_n) : H^n \to H$ is an isometry. We prove that every isometric $n$-tuple is hyperreflexive, in the sense of…

We show that if a tuple of commuting, bounded linear operators $(T_1,...,T_d) \in B(X)^d$ is both an $(m,p)$-isometry and a $(\mu,\infty)$-isometry, then the tuple $(T_1^m,...,T_d^m)$ is a $(1,p)$-isometry. We further prove some additional…

Let $T\colon H\to H$ be a bounded operator on Hilbert space. We say that $T$ has a polygonal type if there exists an open convex polygon $\Delta\subset {\mathbb D}$, with $\overline{\Delta}\cap{\mathbb T}\neq\emptyset$, such that the…

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 results have been extended to q-commuting tuples. We are able to do this when…

A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…

The main result is a test function style commutant lifting theorem for an annulus A. The test functions are the minimal inner functions for A. The model space is the Sarason Hardy Hilbert space for A uniquely determined by the fact that its…

We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting, commuting and non-commuting dilations,…

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…

This paper provides a homotopical version of the adjoint lifting theorem in category theory, allowing for Quillen equivalences to be lifted from monoidal model categories to categories of algebras over colored operads. The generality of our…