On the semi-Browder spectrum (original) (raw)

On Closed Upper and Lower Semi-Browder Operators

Mediterranean Journal of Mathematics, 2014

We give several necessary and sufficient conditions for a closed operator to be upper (lower) semi-Browder. We also apply these results to give some characterizations of upper (lower) semi-Browder spectrum.

Semi-fredholm and semi-browder spectra for Co-quasi-semigroups

Boletim da Sociedade Paranaense de Matemática

In [5] D. Barcenas and H. Leiva are introduced the notion of C0-quasi-semigroups of bounded linear operators, as a generalization of C0-semigroups of operators. In this paper, we shall show the connections between a different spectra of the C0-quasi-semigroups by the spectra of their generators, specially, ascent, descent essential ascent and essential descent, upper and lower semi-Fredholm and semi-Browder spectra.

Some characterizations of operators satisfying a-Browder's theorem

Journal of Mathematical Analysis and Applications, 2005

We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C. Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λI − T . 531 denote the class of all upper semi-Fredholm operators, and let Φ − (X) := T ∈ L(X): β(T ) < ∞ denote the class of all lower semi-Fredholm operators. The class of all semi-Fredholm operators is defined by

Browder and semi-browder operators

Acta Mathematica Scientia, 2012

In this article, we study characterization, stability, and spectral mapping theorem for Browder's essential spectrum, Browder's essential defect spectrum and Browder's essential approximate point spectrum of closed densely defined linear operators on Banach spaces.

The Intersection of Upper and Lower Semi-Browder Spectrum of Upper-Triangular Operator Matrices

Abstract and Applied Analysis, 2013

WhenA∈B(H)andB∈B(K)are given, we denote byMCthe operator acting on the infinite-dimensional separable Hilbert spaceH⊕Kof the formMC=(AC0B). In this paper, it is proved that there exists some operatorC∈B(K,H)such thatMCis upper semi-Browder if and only if there exists some left invertible operatorC∈B(K,H)such thatMCis upper semi-Browder. Moreover, a necessary and sufficient condition forMCto be upper semi-Browder for someC∈G(K,H)is given, whereG(K,H)denotes the subset of all of the invertible operators ofB(K,H).

Browder's theorems and the spectral mapping theorem

Divulgaciones Matematicas

A bounded linear operator T 2 L(X) on a Banach space X is said to satisfy Browder's theorem if two important spectra, originating from Fredholm theory, the Browder spectrum and the Weyl spectrum, coin- cide. This expository article also concerns with an approximate point version of Browder's theorem. A bounded linear operator T 2 L(X) is said to satisfy a-Browder's theorem if the upper semi-Browder spec- trum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. This paper also deals with the relationships between Browder's theorem, a-Browder's theorem and the spectral mapping theorem for certain parts of the spectrum.

Semi-Fredholm Operators with Finite Ascent or Descent and Perturbations

Proceedings of the American Mathematical Society, 1995

In this note we prove that the collection of upper (lower) semi-Fredholm operators with finite ascent (descent) is closed under commuting operator perturbations that belong to the perturbation class associated with the set of upper (lower) semi-Fredholm operators. Then, as a corollary we get the

Some geometric characteristics and perturbations of semi-Fredholm operators

Filomat, 2016

We consider some geometric characteristics of bounded operators on Banach spaces concerning the sets of upper and lower semi-Browder operators and left and right Browder operators. Using various operational quantities we give some perturbation results for upper and lower semi-Fredholm, Weyl and semi-Browder operators as well as for left and right Fredolm, Weyl and Browder operators.