相关论文: Spectral properties of weighted composition operat…

We obtain a complete description of semi-Fredholm spectra of operators of the form $(Tf)(z) = w(z)f(B(z)$ acting on the disc algebra in the case when $B$ is either elliptic or double parabolic finite Blaschke product of degree $d \geq 2$…

In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a {\em…

We study the spectrum of operators $aT\in B(H)$ on a Hilbert space $H$ where $T$ is an isometry and $a$ belongs to a commutative $C^*$-subalgebra $C(X)\cong A\subseteq B(H)$ such that the formula $L(a)=T^*aT$ defines a faithful transfer…

In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces…

For a linear operator $T$ in a Banach space let $\sigma_p(T)$ denote the point spectrum of $T$, $\sigma_{p[n]}(T)$ for finite $n > 0$ be the set of all $\lambda \in \sigma_p(T)$ such that $\dim \ker (T - \lambda) = n$ and let…

A characterization of those points in the unit disc which belong to the spectrum of a composition operator $C_{\varphi}$, defined by a rotation $\varphi(z)=rz$ with $|r|=1$, on the space $H_0(\mathbb{D})$ of all analytic functions on the…

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

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…

Let $\mathcal{T}_{+}(E)$ be the tensor algebra of a $W^{*}$-correspondence $E$ over a $W^{*}$-algebra $M$. In earlier work, we showed that the completely contractive representations of $\mathcal{T}_{+}(E)$, whose restrictions to $M$ are…

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…

This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and…

We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when the map $\varphi$ is a non-invertible homeomorphism of $K$ into itself.

We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…

We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…

In this article, we study the complex symmetry of compositions operators $C_{\phi}f=f\circ \phi$ induced on weighted Bergman spaces $A^2_{\beta}(\mathbb{D}),\ \beta\geq -1,$ by analytic self-maps of the unit disk. One of ours main results…

This paper investigates the spectral properties of Toeplitz operators on the Bergman space of unit disk. We present an integral representation of $ T^*_{z^m}$, which establishes a connection between the Bergman functions and the solutions…

Let $M$ be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of $M$, and we derive a formula for the…

This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…

We prove that the spectrum of every Rota-Baxter operator of weight $\lambda$ on a unital algebraic (not necessarily associative) algebra over a field of characteristic zero is a subset of $\{0,-\lambda\}$. For a finite-dimensional unital…