On the largest analytic set for cyclic operators.
On the local spectral properties of weighted shift operators
We study the local spectral properties of both unilateral and bilateral weighted shift operators.
On the local spectral radius in partially ordered Banach spaces
On the orbits of an operator with spectral radius one
On the poles of the local resolvent.
On the structure of the wave operators in one dimensional potential scattering.
On the weak decomposition property
We study a new class of bounded linear operators which strictly contains the class of bounded linear operators with the decomposition property (δ) or the weak spectral decomposition property (weak-SDP). We treat general local spectral properties for operators in this class and compare them with the case of operators with (δ).
On totally -paranormal operators
In this paper we study some properties of a totally -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally -paranormal operators through the local spectral theory. Finally, we show that every totally -paranormal operator satisfies an analogue of the single valued extension property for and some of totally -paranormal operators have scalar extensions....
On w-hyponormal operators
We study some properties of w-hyponormal operators. In particular we show that some w-hyponormal operators are subscalar. Also we state some theorems on invariant subspaces of w-hyponormal operators.
Open set of eigenvalues and SVEP
Operators on a Hilbert space similar to a part of the backward shift of multiplicity one
Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product . For b, c ∈ X, a weak resolvent of A is the complex function of the form . We will discuss an equivalent condition, in terms of weak resolvents, for A to be similar to a restriction of the backward shift of multiplicity 1.
Operators with an ergodic power
We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
Perturbations of operators satisfying a local growth condition.
Polaroid type operators under perturbations
A bounded operator T defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The "polaroid" condition is related to the conditions of being left polaroid, right polaroid, or a-polaroid. In this paper we explore all these conditions under commuting perturbations K. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for T + K, where K is an...
Properties and applications of the local functional calculus.
Propriétés spectrales des restrictions d’opérateurs de la classe
Some spectral inequalities involving generalized scalar operators
In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu, Barnes,...
Spectra originating from semi-B-Fredholm theory and commuting perturbations
Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used by Burgos et...
Spectral mapping theorems and stability theory in linear dynamical systems.
Stability of the local spectrum.