Altay, Bilâl; Başar, Feyzi On the fine spectrum of the difference operator \(\Delta\) on \(c_{0}\) and \(c\). (English) Zbl 1085.47041 Inf. Sci. 168, No. 1-4, 217-224 (2004). The authors use the methods of functional analysis to study the spectrum of the difference operator \(\Delta\) (\(\Delta x_k:=x_k-x_{k-1}\)) represented by the associated infinite two-diagonal matrix. Reviewer: Roman Hilscher (Brno) Cited in 2 ReviewsCited in 58 Documents MSC: 47B39 Linear difference operators 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46B45 Banach sequence spaces 39A70 Difference operators 47A10 Spectrum, resolvent Keywords:difference operator; fine spectrum; sequence spaces; Mercerian theorem PDFBibTeX XMLCite \textit{B. Altay} and \textit{F. Başar}, Inf. Sci. 168, No. 1--4, 217--224 (2004; Zbl 1085.47041) Full Text: DOI References: [1] A.M. Akhmedov, F. Başar, On the fine spectrum of the Cesàro operator in \(c_0\); A.M. Akhmedov, F. Başar, On the fine spectrum of the Cesàro operator in \(c_0\) [2] J.P. Cartlidge, Weighted mean matrices as operators on \(ℓ^p\); J.P. Cartlidge, Weighted mean matrices as operators on \(ℓ^p\) [3] Goldberg, S., Unbounded Linear Operators (1985), Dover Publications, Inc: Dover Publications, Inc New York [4] Gonzàlez, M., The fine spectrum of the Cesàro operator in \(ℓp(1<p<∞)\), Arch. Math, 44, 355-358 (1985) · Zbl 0568.47021 [5] Kreyszig, E., Introductory Functional Analysis with Applications (1978), John Wiley & Sons Inc: John Wiley & Sons Inc New York, Chichester, Brisbane, Toronto · Zbl 0368.46014 [6] Maddox, I. J., Elements of Functional Analysis (1970), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0193.08601 [7] Okutoyi, J. T., On the spectrum of \(C_1\) as an operator on bv, Commun. Fac. Sci. Univ. Ank. Ser. \(A_1, 41, 197-207 (1992)\) · Zbl 0831.47020 [8] Reade, J. B., On the spectrum of the Cesaro operator, Bull. Lond. Math. Soc, 17, 263-267 (1985) · Zbl 0548.47017 [9] A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies 85, Amsterdam, New York, Oxford, 1984; A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies 85, Amsterdam, New York, Oxford, 1984 · Zbl 0531.40008 [10] Yıldırım, M., On the spectrum and fine spectrum of the compact Rhally operators, Indian J. Pure Appl. Math, 27, 8, 779-784 (1996) · Zbl 0859.47004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.