<abstract xmlns="http://www.w3.org/1999/xhtml">Let (<italic>C</italic>(<italic>t))t</italic>∈𝕉 be a strongly continuous cosine family and <italic>A</italic> be its infinitesimal generator. In this work, we prove that, if <italic>C</italic>(<italic>t</italic>) – coshλ<italic>t</italic> is Saphar (resp. quasi-Fredholm) operator and λ<italic>t</italic> /∉<italic>iπ</italic>𝕑, then <italic>A –</italic> λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.</abstract>

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Department of Mathematics and Computer Science, Pluridisciplinary Faculty of Nador

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp....

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Published Online: Nov 22, 2020

Page range: 80 - 87

Received: Aug 08, 2020

Accepted: Nov 08, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0008

Keywords
Cosine, Quasi-Fredholm, Semi-regular, Saphar

© 2020 Hamid Boua, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Published Online: Nov 22, 2020

Page range: 80 - 87

Received: Aug 08, 2020

Accepted: Nov 08, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0008

KeywordsCosine, Quasi-Fredholm, Semi-regular, Saphar

© 2020 Hamid Boua, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Cosine, Quasi-Fredholm, Semi-regular, Saphar