Related papers: On Weak Supercyclicity II
In this work a possibility of a decomposition of a bounded operator which acts in a Hilbert space $H$ as a product of a J-unitary and a J-self-adjoint operators is studied, $J$ is a conjugation (an antilinear involution). Decompositions of…
In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…
Recently an operator space version of type and cotype, namely type $(p,H)$ and cotype $(q,H)$ of operator spaces for $1\leq p \leq 2\leq q \leq \infty$ and a subquadratic and homogeneous Hilbetian operator space $H$ were introduced and…
In this paper, we will study some properties of b-weakly compact operators and we will investigate their relationships to some variety of operators on the normed vector lattices. With some new conditions, we show that the modulus of an…
Let M\"{o}b denote the group of biholomorphic automorphisms of the unit disc and $(\mbox{M\"{o}b} \cdot T)$ be the orbit of a Hilbert space operator $T$ under the action of M\"{o}b. If the quotient $(\mbox{M\"{o}b} \cdot T)/\sim$, where…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some…
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…
Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property called ultra hypercyclicity and compare it to strong…
In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded…
Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a (bounded or unbounded) scalar type spectral operator $A$ in a complex Banach space as well as of the…
In 2008, J. Parcet showed the $(1,1)$ weak-boundedness of Calder\'on-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections…
We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers,…
A main objective of the present paper is to develop the theory of hypercyclicity and supercyclicity of linear operators on topological vector space over non-Archimedean valued fields. We show that there does not exist any hypercyclic…
In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if $x\in {\mathcal H}$ has a disk…
We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.
In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…
We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…