Related papers: Orthogonal decompositions and twisted isometries I…

We introduce and study doubly twisted near-isometries. A doubly twisted near-isometry is a tuple of near-isometries satisfying certain relations determined by a prescribed family of unitaries, thereby generalizing the notion of doubly…

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…

Let $n > 1$. Let $\{U_{ij}\}_{1 \leq i < j \leq n}$ be $\binom{n}{2}$ commuting unitaries on some Hilbert space $\mathcal{H}$, and suppose $U_{ji} := U_{ij}^*$, $1 \leq i < j \leq n$. An $n$-tuple of isometries $V = (V_1, \ldots ,V_n)$ on…

This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. As a consequence, we obtain Wold-type decomposition for pairs of doubly twisted isometries and in particular, new and simple proof of…

Three canonical decompositions concerning commuting pair of isometries, power partial isometries, and contractions are reassessed. They have already been proved in von Neumann algebras. In the corresponding proofs, both norm and weak…

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…

Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C*-correspondences over N^k, generalising the classical result for a doubly commuting pair of isometries due…

Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of commutant lifting theorem, we introduce a class, denoted by $\mathcal{P}_n(\mathcal{H})$, of $n$-tuples of commuting contractions on a Hilbert space $\mathcal{H}$. We…

We establish a Wold-type decomposition for isometric and isometric Nica-covariant representations of the odometer semigroup. These generalize the Wold-type decomposition for commuting pairs of isometries due to Popovici and for pairs of…

It is well-known that an $n$-tuple $(n\ge 3)$ of commuting contractions does not posses an isometric dilation, in general. Considering a class of $n$-tuple of commuting contractions satisfying certain positivity assumption, we construct…

We investigate Wold-type decompositions and unitary extension problems for multivariable isometric covariant representations associated with product systems of $C^*$-correspondences. First, we establish an operator-theoretic…

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…

S{\l}oci\'nski gave sufficient conditions for commuting isometries to have a nice Wold-like decomposition. In this note we provide analogous results for row-isometries satisfying certain commutation relations. Other than known results for…

We consider the classification, up to unitary equivalence, of commuting n-tuples of isometries. We pay special attention to the case when the product of the isometries is a shift of finite multiplicity, and we provide a complete…

Let $n \geq 2$, and let $V=(V_1,\dots, V_n)$ be an $n$-tuple of isometries acting on a Hilbert space $\mathcal{H}$. We say that $V$ is an $n$-tuple of isometries with equal range if $V_i^{m_i}V_j^{m_j}\mathcal{H} = V_j^{m_j}…

The goal of the paper is to study the structure of the k-tuples of doubly $\Lambda$-commuting row isometries and the $C^*$-algebras they generate from the point of view of noncommutative multivariable operator theory. We obtain Wold…

We show that every multivariable contractive weighted shift dilates to a tuple of commuting unitaries, and hence satisfies von Neumann's inequality. This answers a question of Lubin and Shields. We also exhibit a closely related $3$-tuple…

Motivated by the classical type decomposition of von Neumann algebras, and various more recent extensions to other structures, we develop a type decomposition theory for general posets.

In this article, we prove that any pair of doubly commuting $2$-isometries on a Hilbert space has a Wold-type decomposition. Moreover, the analytic part of the pair is unitary equivalent to the pair of multiplication by coordinate function…

We extend some of the results of Agler, Knese, and McCarthy [1] to $n$-tuples of commuting isometries for $n>2$. Let $\mathbb{V}=(V_1,\dots,V_n)$ be an $n$-tuple of a commuting isometries on a Hilbert space and let Ann$(\mathbb{V})$ denote…