Furkan, Hasan; Bilgiç, Hüseyin; Başar, Feyzi On the fine spectrum of the operator \(B(r,s,t)\) over the sequence spaces \(\ell_p\) and \(bv_p\),(\(1<p<\infty \)). (English) Zbl 1222.47050 Comput. Math. Appl. 60, No. 7, 2141-2152 (2010). The authors determine the exact location of the fine spectrum of a linear operator given by an infinite three-diagonal banded matrix in the sequence spaces \(\ell_p\) and \(bv_p\) for \(p\in(1,\infty)\). Their results generalize some earlier results of the authors and their collaborators on this subject. Reviewer: Roman Šimon Hilscher (Brno) Cited in 1 ReviewCited in 33 Documents MSC: 47B39 Linear difference operators 40C05 Matrix methods for summability 46B45 Banach sequence spaces Keywords:spectrum of an operator; difference operator; generalised difference operator; spectral mapping theorem; sequence spaces \(\ell_p\) and \(bv_p\) PDFBibTeX XMLCite \textit{H. Furkan} et al., Comput. Math. Appl. 60, No. 7, 2141--2152 (2010; Zbl 1222.47050) Full Text: DOI References: [1] Kreyszig, E., Introductory Functional Analysis with Applications (1978), John Wiley & Sons Inc.: John Wiley & Sons Inc. New York, Chichester, Brisbane, Toronto · Zbl 0368.46014 [2] Goldberg, S., Unbounded Linear Operators (1985), Dover Publications, Inc.: Dover Publications, Inc. New York [3] Gonzàlez, M., The fine spectrum of the Cesàro operator in \(\ell_p(1 < p < \infty)\), Arch. Math., 44, 355-358 (1985) · Zbl 0568.47021 [4] J.P. Cartlidge, Weighted mean matrices as operators on \(\ell^p\); J.P. Cartlidge, Weighted mean matrices as operators on \(\ell^p\) [5] Okutoyi, J. T., On the spectrum of \(C_1\) as an operator on \(b v_0\), J. Aust. Math. Soc. Ser. A, 48, 79-86 (1990) · Zbl 0691.40004 [6] Okutoyi, J. T., On the spectrum of \(C_1\) as an operator on \(b v\), Commun. Fac. Sci. Univ. Ank. Sér. A1, 41, 197-207 (1992) · Zbl 0831.47020 [7] Altay, B.; Başar, F., On the fine spectrum of the difference operator on \(c_0\) and \(c\), Inform. Sci., 168, 217-224 (2004) · Zbl 1085.47041 [8] Altay, B.; Başar, F., On the fine spectrum of the generalized difference operator \(B(r, s)\) over the sequence spaces \(c_0\) and \(c\), Int. J. Math. Math. Sci., 2005, 18, 3005-3013 (2005) · Zbl 1098.39013 [9] Kayaduman, K.; Furkan, H., The fine specta of the difference operator \(\Delta\) over the sequence spaces \(\ell_1\) and \(b v\), Int. Math. Forum, 1, 24, 1153-1160 (2006) · Zbl 1119.47306 [10] Akhmedov, A. M.; Başar, F., On the spectra of the difference operator \(\Delta\) over the sequence space \(\ell_p\), Demonstratio Math., 39, 3, 585-595 (2006) · Zbl 1118.47303 [11] Akhmedov, A. M.; Başar, F., On the fine spectra of the difference operator \(\Delta\) over the sequence space \(b v_p, 1 \leqslant p < \infty \), Acta Math. Sin. (Engl. Ser.), 23, 10, 1757-1768 (2007) · Zbl 1134.47025 [12] Furkan, H.; Bilgiç, H.; Kayaduman, K., On the fine spectrum of the generalized difference operator \(B(r, s)\) over the sequence spaces \(\ell_1\) and \(b v\), Hokkaido Math. J., 35, 897-908 (2006) [13] Furkan, H.; Bilgiç, H.; Altay, B., On the fine spectrum of the operator \(B(r, s, t)\) over \(c_0\) and \(c\), Comput. Math. Appl., 53, 6, 989-998 (2007) · Zbl 1124.47024 [14] Bilgiç, H.; Furkan, H., On the fine spectrum of the operator \(B(r, s, t)\) over the sequence spaces \(\ell_1\) and \(b v\), Math. Comput. Modelling, 45, 7-8, 883-891 (2007) · Zbl 1152.47024 [15] Bilgiç, H.; Furkan, H., On the fine spectrum of the generalized difference operator \(B(r, s)\) over the sequence spaces \(\ell_p\) and \(b v_p(1 < p < \infty)\), Nonlinear Anal., 68, 3, 499-506 (2008) · Zbl 1139.47005 [16] Altay, B.; Başar, F., On the space of sequences of \(p\)-bounded variation and related matrix mappings, Ukrainian Math. J., 55, 1, 136-147 (2003) · Zbl 1040.46022 [17] Imaninezhad, M.; Miri, M. R., The dual space of the sequence space \(b v_p,(1 \leqslant p < \infty)\), Acta Math. Univ. Comenian., 79, 1, 143-149 (2010) · Zbl 1212.46023 [18] Choudhary, B.; Nanda, S., Functional Analysis with Applications (1989), John Wiley & Sons Inc.: John Wiley & Sons Inc. New York, Chichester, Brisbane, Toronto, Singapore · Zbl 0698.46001 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.