Related papers: Reducing subspaces of $C_{00}$ contractions
In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroups to the case of bounded $C_0$-semigroups, involving adjoint theory for this class of operators. This approach considerably reduces the…
We show that truncated Toeplitz operators are characterized by a collection of complex symmetries. This was conjectured by Klis-Garlicka, Lanucha, and Ptak, and proved by them in some special cases.
This paper generalizes the classical Sz.-Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots, T_d)$ of commuting bounded…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
We use a theorem by Gonzalez, Leon-Saavedra and Montes-Rodriguez to construct a class of coanalytic Toeplitz operators which have an infinite-dimensional closed subspace, where any non-zero vector is hypercyclic.
This manuscript is an effort to extend the Sz.-Nagy--Foias dilation and model theory for a single contraction to the case of commuting pair of contractions. Fundamental to the Sz.-Nagy--Foias model theory is the functional model for the…
In this article, by considering $T=(T_1,\dots, T_d)$, an $d$-tuple of commuting contractions on a Hilbert space $\mathcal{H}$, we study $T$-Toeplitz operators which consists of bounded operators $X$ on $\mathcal{H}$ such that \[ T_i^*XT_i=X…
Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive $C_{0}$-semigroups under the topology of uniform weak operator convergence on compact subsets of $\mathbb{R}_{+}$.…
This paper investigates whether some fixed point theorems for quasi-contractions on metric spaces introduced by \`Cir\`ic in [1] and generalised by Kumam et al. in [2] can be improved further. It turns out that the answer is negative. We…
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator $T$ can be dilated to a unitary $\cU$. A more general multivariable setting for these ideas is the setup where (i) the unit disk is replaced by a domain…
Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study…
A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\ow)^{-1}$ for $|z|, |w| < 1$, by means of…
We extend results on compressed Toeplitz operators on the backward shift invariant subspaces of $H^2 $ to the context of the spaces $H^p$, $1<p<\infty.$
In the literature, we have several results associated with canonical decomposition of commuting contractions. In this paper, we generalize a few of these results to $Q$-commuting contractions. Here we mainly deal with $Q$-commuting and…
This article develops several functional models for a given $\Gamma_n$-contraction. The first model is motivated by the Douglas functional model for a contraction. We then establish factorization results that clarify the relationship…
We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…
One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces. In this note we generalize this framework to allow the Bergman and…
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of…
A tuple of commuting Hilbert space operators $(S_1, \dots, S_{n-1}, P)$ having the closed symmetrized polydisc \[ \Gamma_n = \left\{ \left(\sum_{i=1}^{n}z_i, \sum\limits_{1\leq i<j\leq n} z_iz_j, \cdots, \prod_{i=1}^{n}z_i\right) :…