Related papers: On subspaces diskcyclicity

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can…

A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.

We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…

In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in the complement of a set $Y\subset\mathbb{N}^d$ with the property that $Y+e_j\subset Y$ for all $j=1,\dots,d$. This is an easy…

This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…

In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.

We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…

We study Dirichlet-type spaces $\mathfrak{D}_{\alpha}$ of analytic functions in the unit bidisk and their cyclic elements. These are the functions $f$ for which there exists a sequence $(p_n)_{n=1}^{\infty}$ of polynomials in two variables…

Let $T$ be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of $T$, it is proved that every operator in the commutant of $T$ is not unicellular. In particular, $T$ has…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on…

In this paper, we investigate the properties of disjoint Ces$\grave{a}$ro-hypercyclic operators. First, the definition of disjoint Ces$\grave{a}$ro-hypercyclic operators is provided, and disjoint Ces$\grave{a}$ro-Hypercyclicity Criterion is…

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…

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…

Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied.…

We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…

We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear counterpart but which is still strong enough to impose linear restrictions on operator space…

We give definitions and some properties of the shift operator S_{L(H^2)} and multiplication operator on L(H^2). In addition, we obtain some properties of the commutant of the shift operator S_{L(H^2)} and characterize S_{L(H^2)}-invariant…