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The fine spectra of the difference operator Δ over the sequence space bv p , (1p<) * . (English) Zbl 1134.47025
The authors find the spectrum of the operator Δ=I-S acting on the sequence space bv p (1p<), S being the canonical translation operator on bv p .
MSC:
47B39Difference operators (operator theory)
47A10Spectrum and resolvent of linear operators
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
References:
[1]Kreyszig, E.: Introductory Functional Analysis with Applications, John Wiley & Sons Inc. New York- Chichester-Brisbane-Toronto, 1978
[2]Goldberg, S.: Unbounded Lineer Operators, Dover Publications Inc. New York, 1985
[3]Wenger, R. B.: The fine spectra of Hölder summability operators. Indian J. Pure Appl. Math., 6, 695–712 (1975)
[4]Reade, J. B.: On the spectrum of the Cesaro operator. Bull. Lond. Math. Soc., 17, 263–267 (1985) · Zbl 0563.47023 · doi:10.1112/blms/17.3.263
[5]Gonzàlez, M.: The fine spectrum of the Cesàro operator in p (1 < p < . Arch. Math., 44, 355–358 (1985) · Zbl 0568.47021 · doi:10.1007/BF01235779
[6]Okutoyi, J. T.: On the spectrum of C 1 as an operator on bv. Commun. Fac. Sci. Univ. Ank., Ser. A1, 41, 197–207 (1992)
[7]Yıldırım, M.: On the spectrum and fine spectrum of the compact Rhally operators. Indian J. Pure Appl. Math., 27(8), 779–784 (1996)
[8]Coşkun, C.: The spectra and fine spectra for p-Cesàro operators. Turkish J. Math., 21, 207–212 (1997)
[9]Akhmedov, A. M., Başar, F.: On spectrum of the Cesaro operator. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 19, 3–8 (2003)
[10]Akhmedov, A. M., Başar, F.: On the fine spectrum of the Cesàro operator in c 0. Math. J. Ibaraki Univ., 36, 25–32 (2004) · Zbl 1096.47031 · doi:10.5036/mjiu.36.25
[11]de Malafosse, B.: Properties of some sets of sequences and application to the spaces of bounded difference sequences of order μ. Hokkaido Math. J., 31, 283–299 (2002)
[12]Altay, B., Başar, F.: On the fine spectrum of the difference operator on c 0 and c. Inform. Sci., 168, 217–224 (2004)
[13]Akhmedov, A. M., Başar, F.: On the fine spectra of the difference operator Δ over the sequence space p , (1 p < . Demonstratio Math., 39 (2006), to appear
[14]Altay, B., Başar, F.: On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces c 0 and c. Internat. J. Math. & Math. Sci., 18, 3005–3013 (2005) · Zbl 1098.39013 · doi:10.1155/IJMMS.2005.3005
[15]Başar, F., Altay, B.: On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math. J., 55(1), 136–147 (2003) · Zbl 1040.46022 · doi:10.1023/A:1025080820961
[16]Wilansky, A.: Summability through Functional Analysis, North-Holland Mathematics Studies, 85, Amsterdam- New York-Oxford, 1984