相关论文: Models for q-commutative tuples of isometries

We represent and classify pairs of commuting isometries $(V_1, V_2)$ acting on Hilbert spaces that satisfy the condition \[ [V_1^*, V_2] = \text{compact and normal}, \] where $[V_1^*, V_2] := V_1^* V_2 - V_2 V_1^*$ is the cross-commutator…

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…

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…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…

There are considered isometries on a Hilbert space. By the Wold theorem any isometry can be decomposed into a unitary operator and a unilateral shift. For a pair of isometries, even commuting, a maximal subspace reducing one isometry to a…

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 canonical model, analogous to the one for contraction operators, is introduced for bi-isometries, two commuting isometries on a Hilbert space. This model involves a contractive analytic operator-valued function on the unit disk. Various…

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.

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…

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…

It is shown that a pair of Hilbert space operators V and W such that V*W=I (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal basis are replaced with biorthogonal sequences, and it is also…

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 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…

The study of a pair $(V_1,V_2)$ of commuting isometries is a classical theme. We shine new light on it by using the defect operator. In the cases when the defect operator is zero or positive or negative, or the difference of two mutually…

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these…

In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(\mu)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have…

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed…

We consider pairs of operators $A,B\in B(H)$, where $H$ is a Hilbert space, such that there exist a linear isometry $f$ from the span of $\{A,B\}$ into $\mathbb{C}^2$ mapping $A,B$ into orthonormal vectors. We prove some necessary…

A pair of Hermitian operators is canonical if they satisfy the canonical commutation relation. It has been believed that no such canonical pair exists in finite-dimensional Hilbert space. Here, we obtain canonical pairs by noting that the…

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…