In the paper we extend some aspects of the essential spectra theory of linear operators acting in non-Archimedean (or p-adic) Banach spaces. In particular, we establish sufficient conditions for the relations between the essential spectra of the sum of two bounded linear operators and the union of their essential spectra. Moreover, we give essential prerequisites by studying the duality between p-adic upper and p-adic lower semi-Fredholm operators. We close this paper by giving some properties of the essential spectra.
A complex number ? is an extended eigenvalue of an operator A if there is a
nonzero operator B such that = ?BA. In this case, B is said to be an
eigenoperator. This research paper is devoted to the investigation of some
results of extended eigenvalues for a closed linear operator on a complex
Banach space. The obtained results are explored in terms two cases bounded,
and closed eigenoperators. In addition, the notion of extended eigenvalues
for a 2 ? 2 upper triangular operator matrix is introduced and some of its
properties are displayed.
In this research paper, we develop some aspects of the theory of Fredholm linear operators acting in p-adic (or non-Archimedean) Banach spaces. In this regard, we establish sufficient conditions for the p-adic Fredholmness of the algebraic sum of unbounded linear operators. Next, we study the perturbation of p-adic upper semi-Fredholm operators under strictly singular operators. Moreover, we give some results concerning quasi-compact and p-adic lower semi-Fredholm operators.
The title has been published incorrectly in the SpringerLink and the correct title is given below.Some results of essential spectra of sum of two bounded linear operators in non-Archimedean Banach space Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.