Browder Essential Spectrum Research Articles

Coperturbation function and lower semi-Browder multivalued linear operators

In this article, we investigate the perturbation theory of lower semi-Browder and Browder linear relations. Our approach is based on the concept of a coperturbation function for linear relations in order to establish some perturbation theorems and deduce the stability under strictly cosingular operator perturbations. Furthermore, we apply the obtained results to study the invariance and the characterization of Browder's essential defect spectrum and Browder's essential spectrum.

Fredholm perturbations and seminorms related to upper semi-Fredholm perturbations

In this paper, we investigate the stability in the set of Fredholm perturbations under composition with bounded operators. Moreover, we introduce the concept of a measure of non-Fredholm perturbations, which allows us to give a general approach to the question of obtaining perturbation theorems for semi-Fredholm operators. Finally, we prove some localization results about the Wolf, the Schechter and the Browder essential spectrum of bounded operators on a Banach space X.

Browder and semi-browder operators

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.

On the Browder essential spectrum of a linear relation

On the Browder essential spectrum of a linear relation

L p spectral independence of the streaming operator

The Lp spectrum of the streaming operator in spherical geometry with detailed balancing wall is discussed. First, the Lp-independence of the spectrum is established. Second, the Browder essential spectrum is proved to be empty except for ∞ under the assumption that the wall is nonmultiplying. Finally, we give a simple example to show that the Lp spectral independence of the operator is not valid if the wall is not detailed balancing.

Approximate point spectrum and commuting compact perturbations

Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B (X) (K(X)). Let σ(A) and σa(A) denote, respectively, the spectrum and approximate point spectrum of an element A of B(X). Setσem(A)and σeb(A) are respectively Schechter's and Browder's essential spectrum of A ([16], [9]). σea (A) is a non-empty compact subset of the set of complex numbers ℂ and it is called the essential approximate point spectrum of A ([13], [14]). In this note we characterize σab(A) and show that if f is a function analytic in a neighborhood of σ(A), then σab(f(A)) = f(σab(A)). The relation between σa(A) and σeb(A), that is exhibited in this paper, resembles the relation between the σ(A) and the σeb(A), and it is reasonable to call σab(A) Browder's essential approximate point spectrum of A.

The Variation of Browder's Essential Spectrum

The Variation of Browder's Essential Spectrum

The variation of Browder’s essential spectrum

This paper is devoted to giving various conditions concerning small perturbation of linear operators which imply the continuous variation of the Browder essential spectrum in the Hausdorff topology on the complex plane.

A characterization of the Browder spectrum

Several different notions of essential spectra are known. This paper is devoted to giving an equivalent definition of the Browder essential spectrum for bounded operators on Hilbert space. Also, it is shown that the set of all operators with essentially disconnected spectrum is a uniformly dense set.

Ascent, Descent, and Commuting Perturbations

In the present paper we investigate the stability of the ascent and descent of a linear operator $T$ when $T$ is subjected to a perturbation by a linear operator $C$ which commutes with $T$. The domains and ranges of $T$ and $C$ lie in some linear space $X$. The results are used to characterize the Browder essential spectrum of $T$. We conclude with a number of remarks concerning the notion of commutativity used in the present paper.

Ascent, descent, and commuting perturbations

In the present paper we investigate the stability of the ascent and descent of a linear operator T T when T T is subjected to a perturbation by a linear operator C C which commutes with T T . The domains and ranges of T T and C C lie in some linear space X X . The results are used to characterize the Browder essential spectrum of T T . We conclude with a number of remarks concerning the notion of commutativity used in the present paper.

The Weyl essential spectrum

Using a modest geometric hypothesis the main theorem of these results classifies the Weyl essential spectrum and the Browder essential spectrum according to the standard terminology for the spectrum of a Hilbert space operator.

Spectral Mapping Theorems and Perturbation Theorems for Browder's Essential Spectrum

Spectral Mapping Theorems and Perturbation Theorems for Browder's Essential Spectrum