No abstract

In this article we investigate the essential spectra of a 2 × 2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to determine the essential spectra of two-group transport operators with general boundary conditions in the Banach space L p ([−a, a] × [−1, 1]) × L p ([−a, a] × [−1, 1]), a > 0.

No abstract

In this paper, we investigate the Gustafson, Weidmann, Kato, Wolf, Schechter and Browder essential spectra of a 2×2 block matrix operator defined on a Banach space where entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components under some properties. Furthermore, we give an application to two-group transport equation.

In this article, we give some results on the S‐essential spectra of a linear operator defined on a Banach space. Furthermore, we apply the obtained results to determine the S‐essential spectra of an integro‐differential operator with abstract boundary conditions in the Banach space Lp([−a,a] × [−1,1]),p ≥ 1 and a > 0. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, after a characterization of a class of bounded Fredholm operators on Banach spaces, we investigate the essential spectra of closed, densely defined linear operators on L spaces. The obtained results are used to describe the p essential spectra of one-dimensional transport equations with general boundary conditions. ᮊ

Key words Demicompact linear operator, essential spectrum, Fredholm and semi-Fredholm operators MSC (2010) 47A53In this paper, we present some results on Fredholm and upper semi-Fredholm operators involving demicompact operators. Our results generalize many known ones in the literature, in particular those obtained by Petryshyn in [27] and Jeribi et al. in [1], [22]. They are used to establish a fine description of the Schechter essential spectrum of closed densely defined operators, and to investigate the essential spectrum of the sum of two bounded linear operators defined on a Banach space by means of the essential spectrum of each of the two operators.

No abstract