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 31
Resolvent Conditions and Power Boundedness on Locally Convex Spaces
Abdellah Akrym, Abdeslam El Bakkali, Abdelkhalek Faouzi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
December 12, 2021
March 03, 2046
April 15, 2046

Abstract: In this paper, we present two resolvent conditions for universally bounded operators on locally convex spaces: The Kreiss resolvent condition (see e.g. [4]), and The uniform resolvent condition (see e.g. [7]). We extend some results from the case of Banach spaces to the locally convex spaces. We will connect these conditions to the following condition \sum_{n=1}^{\infty}\left\Vert T^n \right\Vert_{\mathcal{P}} \leq B , (1) which is of course stronger than the power boundedness. More precisely, we extend the result of O. Nevanlinna [7, Proposition 1.3], to the class of ...