Several books have been devoted to the spectral theory and its applications. However, this
volume is very special as compared with the previous ones. For example, the perturbation …

Linear Operators and Their Essential Pseudospectra provides a comprehensive study of
spectral theory of linear operators defined on Banach spaces. The central items of interest in …

The concept of multivalued linear operators—or linear relations—is the one of the most
exciting and influential fields of research in modern mathematics. Applications of this theory …

The concept of the line graph of a given graph is so natural that it has been independently
discovered by many authors. Of course, each author gave it a different name: It was called …

The characterization of bounded essentially semi regular operators in terms of Kato
decomposition of finite type was studied by several authors. In this paper, we extend this …

In this paper, we introduce a generalization of quasi-Fredholm operators [7] to $ k $-quasi-
Fredholm operators on Hilbert spaces for nonnegative integer $ k $. The case when $ k= 0 …

We begin this chapter by presenting the background material that is needed in our work.
Most of this background is drawn from functional analysis and operator theory by giving …

In this paper, we study the essentially semi-regular linear relation operators everywhere
defined in Hilbert space. We establish a Kato-type decomposition of essentially semi-regular …

Let $(T (t)) _ {t\geq 0} $ be an $\alpha $-times integrated semigroup with generator $ A $ on
a Banach space $ X $. In this paper, we show that the spectral mapping theorem holds for …

The theory of measures of noncompactness and measures of weak noncompactness has
many applications in topology, functional analysis, and operator theory. In this chapter, we …