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Research Article

On q−Cesàro Operators: Boundedness, Compactness and Spectra

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Pages 1019-1037 | Received 15 Aug 2020, Accepted 18 May 2021, Published online: 28 Jun 2021

References

  • Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.
  • Sayer, F. P. (1977). The eigenvalue problem for infinite systems of linear equations. Math. Proc. Camb. Phil. Soc. 82(2):269–273. DOI: 10.1017/S0305004100053895.
  • Cesàro, E. (1890). Sur la multiplication des series. Bull. Sci. Math. 14(2):114–120.
  • Bennett, G. (1999). An inequality for Hausdorff means. Houston J. Math. 25:709–743.
  • Bustoz, J., Gordillo, L. F. (2005). q−Hausdorff summability. J. Comput. Anal. Appl. 7:35–48.
  • Akgun, F. A., Rhoades, B. E. (2013). Properties of some q−Hausdorff matrices. Appl. Math. Comput. 219:7392–7397.
  • Aktuglu, H., Bekar, Ş. (2011). q−Cesàro matrix and q−statistical convergence. J. Comput. Appl. Math. 235(16):4717–4723.
  • Bekar, Ş. (2010). q−matrix summability methods. Ph.D. dissertation. Applied Mathematics and Computer Science, Eastern Mediterranean University, Famagusta.
  • Selmanogullari, T., Savas, E., Rhoades, B. E. (2011). On q−Hausdorff matrices. Taiwanese J. Math. 15(6):2429–2437.
  • Yayinga, T., Hazarikab, B., Mursaleen, M. (2021). On sequence space derived by the domain of q−Cesàro matrix in ℓp space and the associated operator ideal. J. Math. Anal. Appl. 493:124453.
  • Brown, A., Halmos, P. R., Shields, A. L. (1965). Cesàro operators. Acta Sci. Math. (Szeged). 26:125–137.
  • Albanese, A. A., Bonet, J., Ricker, W. J. (2015). Spectrum and compactness of the Cesàro operator on weighted ℓp spaces. J. Aust. Math. Soc. 99:287–314.
  • Albanese, A. A., Bonet, J., Ricker, W. J. (2018). The Cesàro operator in weighted ℓ1 spaces. Math. Nachr. 291:1015–1048.
  • Boyd, D. W. (1968). The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged). 29:31–34.
  • Curbera, G. P., Ricker, W. J. (2013). Spectrum of the Cesàro operator in ℓp. Arch. Math. 100:267–271.
  • Curbera, G. P., Ricker, W. J. (2015). The Cesàro operator and unconditional Taylor series in Hardy spaces. Integr. Equations Oper. Theory 83(2):179–195. DOI: 10.1007/s00020-015-2230-9.
  • Leibowitz, G. (1972). Spectra of discrete Cesàro operators. Tamkang J. Math. 3:123–132.
  • Okutoyi, J. I. (1990). On the spectrum of C1 as an operator on bv0. J. Aust. Math. Soc. A 48(1):79–86. DOI: 10.1017/S1446788700035205.
  • Okutoyi, J. T. (1992). On the spectrum of C1 as an operator on bv. Commun. Fac. Sci. Univ. Ank. Series A1. 41:197–207.
  • Prouza, L. (1976). The spectrum of the discrete Cesàro operator. Kybernetika. 12(4):260–267.
  • Reade, J. B. (1985). On the spectrum of the Cesàro operator. Bull. Lond. Math. Soc. 17(3):263–267. DOI: 10.1112/blms/17.3.263.
  • Rhoades, B. E. (1971). Spectra of some Hausdorff operators. Acta Sci. Math. (Szeged). 32:91–100.
  • Leibowitz, G. (1973). Discrete Hausdorff transformations. Proc. Amer. Math. Soc. 38(3):541–544. DOI: 10.1090/S0002-9939-1973-0315508-0.
  • Rhaly, H. C. Jr., (1982). Discrete generalized Cesàro operators. Proc. Amer. Math. Soc. 86(3):405–409. DOI: 10.2307/2044437.
  • Yildirim, M., Durna, N. (2017). The spectrum and some subdivisions of the spectrum of discrete generalized Cesàro operators on ℓp (1<p<∞). J. Inequal. Appl. 2017(1) Art. No. 193:1–13
  • Yildirim, M., Mursaleen, M., Doğan, Ç. (2018). The spectrum and fine spectrum of generalized Rhaly–Cesàro matrices on c0 and c. Oper. Matrices 12(4):955–975. DOI: 10.7153/oam-2018-12-58.
  • Sawano, Y., El-Shabrawy, S. R. (2020). Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces. Monatsh. Math. 192(1):185–224. DOI: 10.1007/s00605-020-01376-w.
  • Yildirim, M. E. (2020). The spectrum and fine spectrum of q−Cesàro matrices with 0<q<1 on c0. Numer. Funct. Anal. Optim. 41(3):361–377.
  • Appell, J., De Pascale, E., Vignoli, A. (2004). Nonlinear Spectral Theory. De Gruyter Series in Nonlinear Analysis and Applications, Vol. 10. Berlin: Walter de Gruyter.
  • Taylor, A. E., Lay, D. C. (1986). Introduction to Functional Analysis, 2nd ed. Malabar, Florida: Robert E. Krieger Publishing Co.
  • Taylor, A. E., Halberg, C. J. A. Jr., (1957). General theorems about a bounded linear operator and its conjugate. J. Reine Angew. Math. 198:93–111.
  • Akhmedov, A. M., El-Shabrawy, S. R. (2011). On the fine spectrum of the operator Δab over the sequence space c. Comput. Math. Appl. 61(10):2994–3002.
  • Akhmedov, A. M., El-Shabrawy, S. R. (2015). Spectra and fine spectra of lower triangular double-band matrices as operators on ℓp,(1≤p<∞). Math. Slovaca 65(5):1137–1152.
  • Akhmedov, A. M., El-Shabrawy, S. R. (2012). Notes on the fine spectrum of the operator Δab over the sequence space c. J. Fract. Calc. Appl. 3(S):1–7.
  • El-Shabrawy, S. R. (2014). Spectra and fine spectra of certain lower triangular double-band matrices as operators on c0. J. Inequal. Appl 2014(1) Art. No. 241:1–9.
  • El-Shabrawy, S. R., Abu-Janah, S. H. (2018). Spectra of the generalized difference operator on the sequence spaces bv0 and h. Linear Multilinear Algebra 66(8):1691–1708. DOI: 10.1080/03081087.2017.1369492.
  • El-Shabrawy, S. R., Sawano, Y. (2020). On the compactness and spectra of the generalized difference operator on the spaces ℓ∞ and bv. Oper. Matrices, in press.
  • Stieglitz, M., Tietz, H. (1977). Matrixtranformationen von Folgenräumen Eine Ergebnisübersicht. Math. Z. 154(1):1–16. DOI: 10.1007/BF01215107.
  • Jakimovski, A., Russell, D. C. (1972). Matrix mappings between BK-spaces. Bull. London Math. Soc. 4(3):345–353. DOI: 10.1112/blms/4.3.345.
  • Wilansky, A. (1984). Summability through Functional Analysis, North-Holland Mathematics Studies, Vol. 85. Amsterdam: North-Holland.

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