Spectra and fine spectra for the upper triangular band matrix U(a0, a1, a2; b0, b1, b2) over the sequence space c0
Keywords:
Upper triangular band matrix, Spectrum, Fine spectrum, Approximate point spectrum, Defect spectrum, Compression spectrumAbstract
The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operator
on the sequence space c0 where b0, b1 , b2 are nonrzero and the nonzero diagonals are the entries of an oscillatory sequence.
References
Akhmedov, A. M., El-Shabrawy, S. R., On the fine spectrum of the operator ∆v over the sequence space c and cp (1 < p < ∞), Appl. Math. Inf. Sci., 5 (3), pp. 635-654, (2011).
Appell, J., Pascale, E. D., Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin, New York, (2004).
Başar, F., Durna, N., Yildirim, M., Subdivisions of the spectra for genarilized difference operator over certain sequence spaces, Thai J. Math., 9 (2), pp. 285—295, (2011).
Das, R., Tripathy, B. C., The spectrum and fine spectrum of the lower triangular matrix B (r, s, t) on the sequence space cs, Songklanakarin J. Sci. Technol., 38 (3), pp. 265-274, (2016).
Das, R., On the spectrum and fine spectrum of the upper triangular matrix U(r1, r2; s1, s2) over the sequence space c0, Afr. Mat. (28), pp. 841-849, (2017).
Das, R., On the fine spectrum of the lower triangular matrix B(r, s) over the Hahn sequence space, Kyungpook Math. J. 57 (3), pp. 441—455, (2017).
Durna, N., Yildirim, M., Subdivision of the spectra for factorable matrices on c0, GU J. Sci., 24 (1), pp. 45-49, (2011).
Durna, N., Subdivision of the spectra for the generalized upper triangular double-band matrices ∆uv over the sequence spaces c0 and c. ADYU Sci., 6 (1), pp. 31-43, (2016).
Goldberg, S., Unbounded Linear Operators. McGraw Hill, New York, (1966).
Gonzalez, M, The fine spectrum of the Ces`aro operator in cp (1 < p < ∞), Arch. Math., 44, pp. 355-358, (1985).
Paul, A., Tripathy, B. C., The spectrum of the operator D(r, 0, 0, s) over the sequence spaces cp and bvp, Hacet. J. Math. Stat., 43 (3), pp. 425-434, (2014).
Paul, A., Tripathy, B. C., The Spectrum of the operator D(r, 0, 0, s) over the sequence space bv0, Georgian Math. J., 22 (3), pp. 421-426, (2015).
Reade, J. B., On the spectrum of the Ces` aro operato, Bull. Lond. Math. Soc., 17, pp. 263-267, (1985).
Rhoades B. E., The fine spectra for weighted mean operators, Pacific J. Math., 104, pp. 263-267, (1983).
Taylor, R. B., Introduction to functional Analysis, John Wiley and Sons, (1980).
Tripathy, B. C., Saikia , P., On the spectrum of the Cesà ro operator C1 on bv ∩ c∞, Math. Slovaca., 63 (3), pp. 563-572, (2013).
Tripathy, B. C., Paul, A., The Spectrum of the operator D(r, 0, 0, s) over the sequence spaces c0 and c, Kyungpook Math. J. 53 (2), pp. 247—256, (2013).
Tripathy, B. C., Das, R., Spectra of the Rhaly operator on the sequence space bv0 ∩ c∞, Bol. Soc. Parana. Math., 32 (1), pp. 263-275, (2014).
Tripathy, B. C., Das, R., Spectrum and fine spectrum of the upper triangular matrix U(r, s) over the sequence space cs, Proyecciones J. Math., 34 (2), pp. 107-125, (2015).
Tripathy, B. C., Das, R., Fine spectrum of the upper triangular matrix U(r, 0, 0, s) over the squence spaces c0 and c, Proyecciones J. Math., 37 (1), pp. 85-101, (2018).
Yildirim, M., On the spectrum of the Rhaly operators on c0 and c, Indian J. Pure Appl. Math., 29, pp. 1301-1309, (1998).
Yildirim, M., The Fine Spectra of the Rhaly Operators on c0, Turkish J. Math., 26(3), pp. 273-282, (2002).
Wenger, R. B., The fine spectra of H¨ older summability operators, Indian J. Pure Appl. Math., 6, pp. 695-712, (1975).
Wilansky, A., Summability Through Functional Analysis, North Holland, (1984).
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