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.     

Characterization of Closed Densely Defined Semi-Browder Linear Operators

In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder’s essential defect spectrum and Browder’s essential approximate point spectrum under finite rank operator perturbations.     

Perturbations Results for Some Classes Related to Browder Linear Relations and Applications

This paper is devoted to the investigation of the perturbation problem of right (left) Browder linear relations and lower (upper) semi-Browder linear relations under commuting compact linear relations. Further, our results are used to show the invariance of Browder’s spectrum.     

Property (R) under Perturbations

Property (R) holds for a bounded linear operator ${T \in L(X)}$ , defined on a complex infinite dimensional Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points λ of the approximate point spectrum for which λI ? T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz, or algebraic perturbations commuting with T.     

LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS

A closed linear relation T in a Banach space X is called left(resp. right) Fredholm if it is upper(resp. lower) semi Fredholm and its range(resp. null space) is topologically complemented in X. We say that T is left(resp. right) Browder if it is left(resp. right)Fredholm and has a finite ascent(resp. descent). In this paper, we analyze the stability of the left(resp. right) Fredholm and the left(resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.     

Perturbation of semi-Browder operators and stability of Browder's essential defect and approximate point spectrum

In the present paper we investigate the stability of closed densely defined semi-Browder operators under operator perturbations that belong to a perturbation class related to compact operators. Furthermore, we apply the obtained results to give a characterization and to study the stability of Browder's essential approximate point spectrum and Browder's essential defect spectrum.     

Essential,Weyl and Browder spectra of unbounded upper triangular operator matrices

This paper is concerned with the spectral properties of the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which the essential spectrum, the Weyl spectrum and the Browder spectrum of such operator matrix, respectively, coincide with the union of the essential spectrum, the Weyl spectrum and the Browder spectrum of its diagonal entries.     

Property (gb) and perturbations

An operator T acting on a Banach space X possesses property (gb) if , where σa(T) is the approximate point spectrum of T, is the essential semi-B-Fredholm spectrum of T and π(T) is the set of all poles of the resolvent of T. In this paper we study property (gb) in connection with Weyl type theorems, which is analogous to generalized Browder?s theorem. Several sufficient and necessary conditions for which property (gb) holds are given. We also study the stability of property (gb) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic and Riesz operators commuting with T.     

Riesz bases for p-subordinate perturbations of normal operators

For a class of unbounded perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without parentheses is obtained under an additional a priori assumption on the spectrum of the perturbed operator. The results are applied to two classes of block operator matrices.     

Browder’s Theorems through Localized SVEP

A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum 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. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds.     

Property (R) for Upper Triangular Operator Matrices

Acta Mathematica Sinica, English Series - Property (R) holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with...     

Ruston,Riesz and perturbation classes

We determine the perturbation classes of Fredholm and Weyl elements, as well the “commuting perturbation classes” of Fredholm, Weyl and Browder elements with respect to unbounded Banach algebra homomorphism T. Among other things we use the Ruston elements of Mouton, Mouton and Raubenheimer. Also, we investigate the class of polynomially almost T null and the class of polynomially T Riesz elements.     

一致可逆性质及广义(ω)性质的摄动

Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.     

Property （ω） and topological uniform descent

We give the necessary and sufficient condition for a bounded linear operator with property （ω） by means of the induced spectrum of topological uniform descent, and investigate the permanence of property （ω） under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.     

Weyl’s Theorem and Perturbations

In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fⁿ is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results for this class.     

Stability of essential spectra of singular Sturm‐Liouville differential operators under perturbations small at infinity

This paper is concerned with the stability of essential spectra of singular Sturm‐Liouville differential operators with complex‐valued coefficients. It is proved that the essential spectrum of the corresponding minimal operator is preserved by perturbations small at infinity with respect to the unperturbed operator. Based on it, 1‐dimensional Schrödinger operators under local dilative perturbations are studied.     

Polynomially Riesz perturbations

In this paper we investigate perturbation of left (right) Fredholm, Weyl and Browder operators by polynomially Riesz operators. We show how Baklouti’s idea of “communication” enhances the perturbation properties of polynomially Riesz operators.     

An Andô-Douglas type theorem in Riesz spaces with a conditional expectation

In this paper we formulate and prove analogues of the Hahn-Jordan decomposition and an Andô-Douglas-Radon-Nikodým theorem in Dedekind complete Riesz spaces with a weak order unit, in the presence of a Riesz space conditional expectation operator. As a consequence we can characterize those subspaces of the Riesz space which are ranges of conditional expectation operators commuting with the given conditional expectation operators and which have a larger range space. This provides the first step towards a formulation of Markov processes on Riesz spaces.