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Research Article

Spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces

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Pages 1157-1175 | Received 13 Jun 2023, Published online: 30 Nov 2023

References

  • A.M. Akhmedov and F. Basar, On the fine spectrum of the Cesàro operator in c0, Mathematical Journal of Ibaraki University 36 (2004), 25–32. doi: 10.5036/mjiu.36.25
  • A.A. Albanese, Spectrum of the Cesàro operator on the Ultradifferentiable Function Spaces ϵω(ℝ+), Complex Analysis and Operator Theory 15 (2021), 1–14. doi: 10.1007/s11785-020-01072-5
  • A.A. Albanese, J. Bonet, and W.J. Ricker, On the continuous Cesàro operator in certain function spaces, Positivity 19 (2015), 659–679. doi: 10.1007/s11117-014-0321-5
  • A.A. Albanese, J. Bonet, and W.J. Ricker, Spectrum and compactness of the Cesàro operator on weighted lp spaces, Journal of the Australian Mathematical Society 99 (2015), 287–314. doi: 10.1017/S1446788715000221
  • A.A. Albanese, J. Bonet, and W.J. Ricker, Dynamics and spectrum of the Cesàro operator on C∞(ℝ+), Monatshefte für Mathematik 181 (2016), 267–283. doi: 10.1007/s00605-015-0863-z
  • A.A. Albanese, J. Bonet, and W.J. Ricker, The Cesáro operator in weighted l1 spaces, Mathematische Nachrichten 291 (2018), 1015–1048. doi: 10.1002/mana.201600509
  • S. Astashkin and L. Maligranda, Interpolation between L1 and L∞, 1 < p < ∞, Proceedings of the American Mathematical Society 132 (2004), 2929–2938. doi: 10.1090/S0002-9939-04-07425-8
  • K.B. Athreya and S.N. Lahiri, Measure theory and probability theory, Vol. 19, Springer, New York, 2006.
  • C. Bennett and R.C. Sharpley, Interpolation of operators, Vol. 129, Academic Press, Boston, 1988.
  • D.W. Boyd, The Hilbert transform on rearrangement-invariant spaces, Canadian Journal of Mathematics 19 (1967), 599–616. doi: 10.4153/CJM-1967-053-7
  • D.W. Boyd, Spaces between a pair of reflexive lebesgue spaces, Proceedings of the American Mathematical Society 18 (1967), 215–219. doi: 10.1090/S0002-9939-1967-0212556-3
  • D.W. Boyd, The spectral radius of averaging operators, Pacific Journal of Mathematics 24 (1968), 19–28. doi: 10.2140/pjm.1968.24.19
  • D.W. Boyd, Spectrum of Cesàro operator, Acta Scientiarum Mathematicarum (Szeged) 29 (1968), 31–34.
  • A. Brown, P.R. Halmos, and A.L. Shields, Cesàro operators, Acta Scientiarum Mathematicarum (Szeged) 26 (1965), 125–137.
  • G.P. Curbera and W.J. Ricker, Spectrum of the Cesàro operator in lp, Archiv der Mathematik 100 (2013), 267–271. doi: 10.1007/s00013-013-0498-z
  • G.P. Curbera and W.J. Ricker, Solid extensions of the Cesàro operator on lp and c0, Integral Equations and Operator Theory 80 (2014), 61–77. doi: 10.1007/s00020-014-2149-6
  • G.P. Curbera and W.J. Ricker, The Cesào operator and unconditional Taylor series in Hardy spaces, Integral Equations and Operator Theory 83 (2015), 179–195. doi: 10.1007/s00020-015-2230-9
  • H.R. Dowson, Spectral theory of linear operators, Vol. 12, Academic Press, London, 1978.
  • M. Gonzàlez, The fine spectrum of the Cesàro operator in lp(1 < p < ∞), Archiv der Mathematik 44 (1985), 355–358. doi: 10.1007/BF01235779
  • K. Jorgens and G.F. Roach, Linear Integral Operators, Pitman, Boston, 1982.
  • S.G. Krein, Yu. Petunin, and E.M. Semenov, Interpolation of linear operators, Vol. 54, American Mathematical Society, Providence, R.I., 1982.
  • G. Leibowitz, Spectra of discrete Cesàro operators, Tamkang Journal of Mathematics 3 (1972), 123–132.
  • G. Leibowitz, Spectra of finite range Cesàro operators, Acta Scientiarum Mathematicarum 35 (1973), 27–29.
  • G. Leibowitz, The Cesàro operators and their generalizations: examples in in finite dimensional linear analysis, The American Mathematical Monthly 80 (1973), 654–661.
  • J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Springer, Berlin, 1979.
  • J.I. Okutoyi, On the spectrum of C1 as an operator on bv0, Journal of the Australian Mathematical Society 48 (1990), 79–86. doi: 10.1017/S1446788700035205
  • J.I. Okutoyi, On the spectrum of C1 as an operator on bv, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 41 (1992), 197–207.
  • J.B. Reade, On the spectrum of the Cesàro operator, Bulletin of the London Mathematical Society 17 (1985), 263–267. doi: 10.1112/blms/17.3.263
  • W. Rudin, Functional Analysis, Vol. 129, McGraw-Hill, New York, 1991.
  • F.G. Tricomi, Integral Equations, Interscience Publishers, Inc., New York, 1957.
  • K.S. Tulenov and G.T. Zaur, Spectrum of the Cesàro-Hardy operator in Lorentz Lp,q(0,1) spaces, Journal of Mathematics, Mechanics and Computer Science 117 (2023), 42–49.

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