Related papers: Kernels of Perturbed Hankel Operators

We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $\Omega \subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For…

An operator $T$ acting on a separable complex Hilbert space $H$ is said to be hypercyclic if there exists $f\in H$ such that the orbit $\{T^n f:\ n\in \mathbb{N}\}$ is dense in $H$. Godefroy and Shapiro \cite{GoSha} characterized those…

We develop a complete Fredholm and invertibility theory for Toeplitz+Hankel operators $T(a)+H(b)$ on the Hardy space $H^p$, $1<p<\infty$, with piecewise continuous functions $a,b$ defined on the unit circle which are subject to the…

Suppose $\mathcal{A}$ is a compact normal operator on a Hilbert space $H$ with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to zero exponentially fast), and let $\mathcal{L}$ be its rank…

The purpose of this paper is to analysis the Harnack part of some truncated shifts whose $\rho$-numerical radius equal one in the finite dimensional case. As pointed out in Theorem 1.17 [12], a key point is to describe the null spaces of…

In this paper we consider Hankel operators on domains with bounded intrinsic geometry. For these domains we characterize the $L^2$-symbols where the associated Hankel operator is compact (respectively bounded) on the space of square…

In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of…

A bounded linear operator $T$ acting on a Hilbert space $\mathcal{H}$ is said to be recurrent if for every non-empty open subset $U\subset \mathcal{H}$ there is an integer $n$ such that $T^n (U)\cap U\neq\emptyset$. In this paper, we…

In this paper, we first introduce $L^{\sigma_1}$-$(\log L)^{\sigma_2}$ conditions satisfied by the variable kernels $\Omega(x,z)$ for $0\leq\sigma_1\leq1$ and $\sigma_2\geq0$. Under these new smoothness conditions, we will prove the…

We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…

We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and…

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…

In the Hardy spaces $H^1$ and $H^\infty$, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when $H^1$ (resp., $H^\infty$) gets replaced by the…

The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…

We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

We present a proof that the operator norm of the commutator of certain spectral projections associated with spin operators converges to $\frac 1 2$ in the semiclassical limit. The ranges of the projections are spanned by all eigenvectors…

In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…