Related papers: The structure of doubly non-commuting isometries

Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under…

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly…

A tuple $\underline{T}=(T_1, \dotsc, T_k)$ of operators on a Hilbert space $\mathcal H$ is said to be \textit{$q$-commuting with} $\|q\|=1$ or simply $q$-\textit{commuting} if there is a family of scalars $q=\{q_{ij} \in \mathbb C :…

A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$…

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and…

For commuting contractions $T_1,\dots ,T_n$ acting on a Hilbert space $\mathcal H$ with $T=\prod_{i=1}^n T_i$, we show that $(T_1, \dots, T_n)$ dilates to commuting isometries $(V_1, \dots , V_n)$ on the minimal isometric dilation space of…

The celebrated Sz.-Nagy and Foias and Ando theorems state that a single contraction, or a pair of commuting contractions, acting on a Hilbert space always possesses isometric dilation and subsequently satisfies the von Neumann inequality…

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 $(T_1,\dots ,T_n)$ dilates to commuting isometries $(V_1,\dots ,V_n)$ on…

An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…

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…

This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…

Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…

The article deals with isometric dilation and commutant lifting for a class of $n$-tuples $(n \geq 3)$ of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a…

Given a bounded operator $Q$ on a Hilbert space $\mathcal{H}$, a pair of bounded operators $(T_1, T_2)$ on $\mathcal{H}$ is said to be $Q$-commuting if one of the following holds: \[ T_1T_2=QT_2T_1 \text{ or }T_1T_2=T_2QT_1 \text{ or…

Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural…

The classical Cowen-Douglas class of (commuting tuples of) operators possessing an open set of (joint) eigenvalues of finite constant multiplicity was introduced by Cowen and Douglas, generalizing the backward shifts. Their unitary…

Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…

We classify tuples of (not necessarily commuting) isometries that admit von Neumann-Wold decomposition. We introduce the notion of twisted isometries for tuples of isometries and prove the existence of orthogonal decomposition for such…

The aim of the present paper is, firstly we study the concepts of (m, (q_1, ..., q_d))- partial isometries on a Hilbert space, secondly, we introduce the notion of m- invertibility of tuples of operators as a natural generalization of the…

We give a new formulation and proof of a theorem of Halmos and Wallen on the structure of power partial isometries on Hilbert space. We then use this theorem to give a structure theorem for a finite set of partial isometries which…