Related papers: Eigenfunctions for Hyperbolic Composition Operator…
This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…
This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of…
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather…
In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables formula. With the same formula, we characterise the bounded…
We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
The semigroup of weighted composition operators $(W_n)_{n\in \mathbb{N}}$, defined by $$W_nf(z)=(1+z+\cdots +z^n)f(z^n),$$ acts on the classical Hardy-Hilbert space $H^{2}(\mathbb{D})$, and exhibits intriguing connections with both the…
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we…
For any real $\beta$ let $H^2_\beta$ be the Hardy-Sobolev space on the unit disc $\mathbb{D}$. $H^2_\beta$ is a reproducing kernel Hilbert space and its reproducing kernel is bounded when $\beta>1/2$. In this paper, we characterize that for…
Let $\phi$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_{\phi}f=f\circ \phi$ on the Hardy space $H^2(\mathbb{D}).$ We mainly characterize all…
We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric…
We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on…
Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_{\varphi}$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.
Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace $H^2$ generated by the limit points in the $H^2$ norm of the orbit of a thin Blaschke product $B$ under composition operators $C_\phi$ induced by…
A closed subspace is invariant under the Ces\`aro operator $\mathcal{C}$ on the classical Hardy space $H^2(\mathbb D)$ if and only if its orthogonal complement is invariant under the $C_0$-semigroup of composition operators induced by the…
We study weighted composition operators on quasi-Banach spaces of holomorphic functions via their induced action on jets along periodic orbits. Under a natural graded nondegeneracy condition, boundedness and compactness, together with a…
In this paper, we study hyponormal weighed composition operators on the Hardy and weighted Bergman spaces. For functions $\psi \in A(\mathbb{D})$ which are not the zero function, we characterize all hyponormal compact weighted composition…
In the present paper, we study the composition operators acting on weighted Hardy spaces of polynomial growth, which are concerned with norms, spectra and (semi-)Fredholmness. Firstly, we estimate the norms of the composition operators with…
Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…
In this paper, the structure of the nearly invariant subspaces for discrete semigroups generated by several (even infinitely many) automorphisms of the unit disc is described. As part of this work, the near $S^*$-invariance property of the…