On q−Cesàro Operators: Boundedness, Compactness and Spectra. (4th July 2021)

• Record Type: Journal Article
• Authors: El-Shabrawy, Saad R.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 9(2021)
• Page Start: 1019
• Page End: 1037
• Publication Date: 2021-07-04
• Subjects: Cesàro operators -- sequence spaces -- spectrum; Primary 47A10 -- Secondary 47B37 -- 46B45; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933027
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The main purpose of the paper is to investigate the spectra of the q − Cesàro operator Cq, where 0 < q < ∞, on Banach spaces. For 0 < q < 1, the method of the proof is to exhibit a relationship between the operator Cq and a generalized difference operator Δ ab . Furthermore, for 1 < q < ∞, it is shown that the operator Cq is compact on certain Banach spaces. In this case, the spectra of Cq are completely determined.