Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 249
Spectrum and Spectral radius of a bb-bounded operator in a topological vector space
Mohamed Lghitous
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 28, 2022
March 03, 2220
April 15, 2220

Abstract: we study the class of bb-bounded linear operators in topological vector spaces, endowed with a topology that we will define. We extend some properties concerning spectral radius, introduced by Troitsky, for this class of operators. We give sufficient conditions for the completeness of the topological vector space of this class of operators. We show that Gelfand's formula for the spectral radius and the Neumann series can be interpreted naturally for bb-bounded operators on topological vector spaces. Finally, as an application, we give sufficient conditions for the invertibility of a ...