When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and ...When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and sufficient conditionson A and B for wh{ch Mc is upper semi-Fredholm with negative index or Weyl for some C C ∈LR（K, H）.展开更多
In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a v...In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.展开更多
In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of clos...In this article, we study characterization, stability, and spectral mapping the- orem 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.展开更多
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation re...In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.展开更多
文摘When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and sufficient conditionson A and B for wh{ch Mc is upper semi-Fredholm with negative index or Weyl for some C C ∈LR（K, H）.
文摘In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.
文摘In this article, we study characterization, stability, and spectral mapping the- orem 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.
文摘In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
