A Spectral Analysis of Linear Operator Pencils on Banach Spaces with Application to Quotient of Bounded Operators

• Main Authors: Bekkai Messirdi, Abdellah Gherbi, Mohamed Amouch
• Format: Article
• Language: English
• Published: Etamaths Publishing 2015-03-01
• Series: International Journal of Analysis and Applications
• Online Access: http://etamaths.com/index.php/ijaa/article/view/440

<span lang="EN-US">Let X and Y two complex Banach spaces and (A,B) a pair of bounded linear</span> operators acting on X with value on Y. This paper is concerned with spectral analysis ofthe pair (A;B): We establish some properties concerning the   spectrum of the linear operator pencils (A-lambda B) when B is not necessarily invertible and lambda is a complex number. Also, we use the functional calculus for the pair (A,B) to prove the corresponding spectral mapping theorem for (A,B). In addition, we de<span lang="EN-US">fi</span><span lang="EN-US">ne the generalized Kato essential spectrum and the closed range spectra of the pair (A,B) and we give some relationships between this spectrums. As application, we describe a spectral analysis of quotient operators.</span>