Related papers: Projections in Toeplitz algebra
In this work, we prove that the product of a function belonging to a Hardy-Orlicz space $H^{\Phi_{1}}$ and a function from another Hardy-Orlicz space $H^{\Phi_{2}}$ belongs to a third Hardy-Orlicz space $H^{\Phi_{3}}$. Moreover, we…
Recently, Liang and Partington \cite{YP} show that kernels of finite-rank perturbations of Toeplitz operators are nearly invariant with finite defect under the backward shift operator acting on the scalar-valued Hardy space. In this article…
We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…
We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3)…
Let $\mu$ be a positive Borel measure on the interval [0,1). The Hankel matrix $\mathcal{H}_\mu= (\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}= \mu_{n+k}$, where $\mu_n=\int_{ [0,1)}t^nd\mu(t)$, induces formally the operator…
This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…
We consider bounded Hankel operators $H_{\psi}$ acting on the Hardy space $H^2$ to $L^2\ominus H^2$ and obtain results on the Schmidt subspaces $E^+_s(H_\psi)$ of such operators defined as the kernels of $ H_{\psi}^{\ast}H_{\psi}-s^2I$…
We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant…
We apply the theory of de Branges-Rovnyak spaces to describe kernels of some Toeplitz operators on the classical Hardy space $H^2$. In particular, we discuss the kernels of the operators $T_{\bar f/ f}$ and $T_{\bar I\bar f/ f}$, where $f$…
We consider cyclic $m$-isometries on a complex separable Hilbert space. Such operators are characterized in terms of shifts on abstract spaces of weighted Dirichlet type. Our results resemble those of Agler and Stankus, but our model spaces…
Our aim in this paper is to obtain necessary and sufficient conditions for weighted shift operators on the Hilbert spaces $\ell^{2}(\mathbb Z)$ and $\ell^{2}(\mathbb N)$ to be subspace-transitive, consequently, we show that the Herrero…
It is well known that a Toeplitz operator is invertible if and only if its symbols admits a canonical Wiener-Hopf factorization, where the factors satisfy certain conditions. A similar result holds also for singular integral operators. More…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. The primary object of this paper is the norm-closed operator algebra generated by a left…
The non-commutative analytic Toeplitz algebra is the weak operator topology closed algebra generated by the left regular representation of the free semigroup on $n$ generators. The structure theory of contractions in these algebras is…
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…
We study Toeplitz operators on the Bargmann space, whose Toeplitz symbols are exponentials of complex inhomogeneous quadratic polynomials. Extending a result by Coburn--Hitrik--Sj\"{o}strand, we show that the boundedness of such Toeplitz…
In the recent paper by Mark C. Ho (2014) the notion of a $\lambda$-Toeplitz operator on the Hardy space $H^2(\mathbb{T})$ over the one-dimensional torus $\mathbb{T}$ was introduced and it was shown (under the supplementary condition) that…
In this note, we define a bounded variant on the Hilbert projective metric on an infinite dimensional space $E$ and study the contraction properties of the projective maps associated with positive linear operators on $E$. More precisely, we…
We study a pair p,e consisting of a projection p (an idempotent) and an effect e (an element between 0 and 1) in a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algebra). We show that some of Halmos's theory…