Related papers: Spectrum of a composition operator with automorphi…
Given a symbol $\varphi,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_{\varphi}(f)=f\circ\varphi$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and…
We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new…
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
It is shown that every component of the spectrum of a weakly hypercyclic operator meets the unit circle. The proof is based on the lemma that a sequence of vectors in a Banach space whose norms grow at geometrical rate doesn't have zero in…
Let $\Omega$ be a bounded symmetric domain except the two exceptional domains of ${\Bbb C}^N$ and $\phi$ a holomorphic self-map of $\Omega.$ This paper gives a sufficient and necessary condition for the composition operator $C_{\phi}$…
We characterize the spectra of composition operators on the Hardy space $H^2(B_N)$, when the symbols are elliptic or hyperbolic linear fractional self-maps of $B_N$. Therefore, combining with the result obtained by Bayart \cite{B10}, the…
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'{e}chet space of the entire mappings that are bounded on bounded sets the composition turns to be…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…
We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…
In this note we study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols $\varphi$ that induce a bounded composition operator…
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently…
Fix a metric space $M$ and let $\mathrm{Lip}_0(M)$ be the Banach space of complex-valued Lipschitz functions defined on $M$. A weighted composition operator on $\mathrm{Lip}_0(M)$ is an operator of the kind $wC_f : g \mapsto w \cdot g \circ…
We characterize the spectrum of positive linear operators $T:X \to Y$, where $X$ and $Y$ are complex Banach function spaces with unit $1$, having finite rank and a partition of unity property. Then all the points in the spectrum are…
In this paper we study the behavior of Hamilton operators and their spectra which depend on infinitely many coupling parameters or, more generally, parameters taking values in some Banach space. One of the physical models which motivate…
The $p$-adic unitary operator $U$ is defined as an invertible operator on $p$-adic ultrametric Banach space such that $\left |U\right |=\left |U^{-1}\right |=1$. We point out $U$ has a spectral measure valued in $\textbf{projection…
Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we define a subset sigma(f,p) of K, called spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in the linear…
The spectrum of a weighted composition operator $C_{\psi, \varphi}$ who is induced by an automorphism has been investigated for over fifty years. However, many results are got only under the condition that the weight function $\psi$ is…
In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.