Related papers: Spectra of Upper-triangular Operator Matrix

Let $M_{C}=\left(\begin{array}{cc}A&C\\0&B\\\end{array} \right)$ is a 2-by-2 upper triangular operator matrix acting on the Banach space $X\oplus Y$ or Hilbert space $H\oplus K$. For the most import spectra such as spectrum, essential…

Let $A\in \mathcal{B}(X)$ and $B\in \mathcal{B}(Y)$, where $X$ and $Y$ are Banach spaces, and let $M_{C}$ be an operator acting on $X\oplus Y$ given by $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}$. We investigate the limit point…

This paper is concerned with general $n\times n$ upper triangular operator matrices with given diagonal entries. We characterize perturbations of the left (right) essential spectrum, the essential spectrum, as well as the left (right) the…

Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$…

We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of…

If $A\in\mathcal{B}(\mathcal{H})$ and $B\in\mathcal{B}(\mathcal{K})$ are given operators, denote by $M_C$ an operator matrix of the form $$M_C=\begin{pmatrix} A & C\\ 0 & B \end{pmatrix}\in\mathcal{B}(\mathcal{H}\oplus\mathcal{K})$$ acting…

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. In particular, it is shown that the spectrum function is Borel from the space of bounded operators on a separable Banach space;…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…

We consider a closure operator $c$ of finite type on the space $SMod(\mathcal M)$ of thick $\mathcal K$-submodules of a triangulated category $\mathcal M$ that is a module over a tensor triangulated category $(\mathcal K,\otimes,1)$. Our…

Let $\mathbb B_n$ be the open unit ball in $\mathbb C^n$. We characterize the spectra of pointwise multipliers $M_u$ acting on Banach spaces of analytic functions on $\mathbb B_n$ satisfying some general conditions. These spaces include…

Let $X$ and $Y$ be Banach spaces such that the ideal of operators which factor through $Y$ has codimension one in the Banach algebra $\mathscr{B}(X)$ of all bounded operators on $X$, and suppose that $Y$ contains a complemented subspace…

In this paper, we study the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which upper semi-Weyl spectrum (resp. upper semi-Browder spectrum) of such operator matrix…

We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.

We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space $l^1$. Some of the results have application in population dynamics.

In this note, we consider the smallest submaximal space structure {\mu}(X) on a Banach space X. We derive a characterization of {\mu}(X) up to complete isometric isomorphism in terms of a universal property. Also, we show that an injective…

We study the spectral synthesis for the Banach *-algebra $A\oop B$, the operator space projective tensor product of $C^*$-algebras $A$ and $B$. It is shown that if $A$ or $B$ has finitely many closed ideals, then $A\oop B$ obeys spectral…

We investigate properties of essential spectra of disjointness preserving operators acting on Banach $C(K)$-modules. In particular, we prove that under some very mild conditions the upper semi-Fredholm spectrum of such an operator is…

The discrete Ces\`aro operator $ C $ acts continuously in various classical Banach sequence spaces within $ \mathbb{C}^{\mathbb{N}}.$ For the coordinatewise order, many such sequence spaces $ X $ are also complex Banach lattices (eg. $c_0,…

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…