In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we es...In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.展开更多
In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unb...In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unbounded 2×2 block operator matrix L_(0)ensuring itsε-pseudo weak demicompactness are provided.In addition,we apply the obtained results to discuss the incidence of some perturbation results on the behavior of essential pseudospectra of L_(0).The results are formulated in terms of some denseness conditions on the topological dual space.展开更多
文摘In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.
文摘In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unbounded 2×2 block operator matrix L_(0)ensuring itsε-pseudo weak demicompactness are provided.In addition,we apply the obtained results to discuss the incidence of some perturbation results on the behavior of essential pseudospectra of L_(0).The results are formulated in terms of some denseness conditions on the topological dual space.
