Related papers: On complex symmetric weighted shifts. II
We study the dynamical behaviour of weighted shifts defined on sequence spaces of a directed tree. In particular, we characterize their boundedness as well as when they are hypercyclic, weakly mixing and mixing.
Criteria for subnormality of unbounded injective weighted shifts on leafless directed trees with one branching vertex are proposed. The case of classical weighted shifts is discussed. The relevance of an inductive limit approach to…
We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operators in question.
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…
We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the…
A formally normal weighted shift on a directed tree is shown to be a bounded normal operator. The question of whether a normal extension of a subnormal weighted shift on a directed tree can be modeled as a weighted shift on some, possible…
We systematically develop the multivariable counterpart of the theory of weighted shifts on rooted directed trees. Capitalizing on the theory of product of directed graphs, we introduce and study the notion of multishifts on directed…
The weighted shifts are long known and important class of operators. One of known generalisation of this class are weighted shifts on directed trees, where we replace the linear order of coordinates in $\ell^2$ with a possibly more…
We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fr\'echet sequence spaces in terms of the existence of a large…
In this paper we investigate a new class of operators called weighted shifts on directed trees introduced recently in [Z. J. Jablonski, I. B. Jung and J. Stochel, A Non-hyponormal Operator Generating Stieltjes Moment Sequences, J. Funct.…
For a given directed tree and weights associated with vertices from a subtree the completion problem is to determine if these weights may be completed in a way to obtain a bounded weighted shift on the whole tree, which possibly satisfies…
Unbounded complex symmetric weighted shifts are studied. Complex symmetric unilateral weighted shifts whose $C^\infty$ vectors contain the image of the canonical orthonormal basis under the conjugation are shown to be decomposable into an…
In this paper we characterise absolutely norm attaining quasi*paranormal weighted shifts on directed trees and give some examples. Moreover we give some examples which show that the spectrum of a positive absolutely norm attaining operator…
We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described…
Recently K.-G. Grosse-Erdmann and D. Papathanasiou described hypercyclic shifts in weighted spaces on directed trees. In this note we discuss several simple examples of graphs which are not trees, e.g., the lattice graphs, and study…
In this paper we initiate the study of the forward and backward shifts on the Hardy space of a tree and the little Hardy space of a tree. In particular, we investigate when these shifts are bounded, find the norm of the shifts if they are…
Inspired by natural classes of examples, we define generalized directed semi-tree and construct weighted shifts on the generalized directed semi-trees. Given an $n$-tuple of directed directed semi-trees with certain properties, we associate…
In a paper from 2012 Jab{\l}o\'nski, Jung and Stochel introduced the weighted shifts on directed trees, a generalisation of well known weighted shift operators on $\ell^2$. In the last decade this class has proven itself handy for finding…