Related papers: Hyperexpansive Weighted Translation Semigroups
We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert space of the solution to the Cauchy problem associated to Gauss-Laguerre invariant Markov semigroups that we introduce. Their generators turn out to be…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
In this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight…
We study the weak limit semigroup of an operator $T$, i.e., the set of all operators being weak limit points of the powers of $T$, in three different but related contexts: Koopman operators of measure-preserving transformations,…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the…
This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with symbols in the H\"ormander classes. Here we prove pointwise…
We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We also present an example of unitary equivalence between shifts defined…
We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…
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…
We systematize and generalize recent results of Gerlach and Gl\"uck on the strong convergence and spectral theory of bounded (positive) operator semigroups $(T_s)_{s\in S}$ on Banach spaces (lattices). (Here, $S$ can be an arbitrary…
We build on the work by Davies, extending the Helffer-Sj\"ostrand Functional Calculus domain for semi-bounded operators on Banach spaces given a priori controlled growth of the resolvents. We employ Seeley's Extension Theorem to extend…
In the first part of this paper we describe the status of the art of this subject. In the second part we present and motivate some new results. Indeed, we introduce some new weighted maximal operators of the partial sums of the…
The goal of this article is to develop a theory for direct integrals of $C_0$-semigroups on Hilbert spaces parallel to the recent approach by Lachowicz and Moszy\'nski for direct sums of Banach spaces, diagonal operators, and semigroups. In…
In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional…
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…
This dissertation summarizes my investigations in operator theory during my PhD studies. The first chapter is an introduction to that field of operator theory which was developed by B. Sz.-Nagy and C. Foias, the theory of power-bounded…
The noncommutative Choquet boundary and the C*-envelope of operator systems of the form Span{1,T,T*}, where T is a Hilbert space operator with normal-like features, are studied. Such operators include normal operators, k-normal operators,…
Quasi-isometric liftings similar to isometries, for the operators similar to contractions in Hilbert spaces, are investigated. The existence of such liftings is established, and their applications are explored for specific operator classes,…
In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.