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Tytuł artykułu

Spectrum and fine spectrum of generalized second order forward difference operator ∆2uvw on sequence space l1

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EN
Abstrakty
EN
The purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator ∆²uvw on sequence space l1. The operator ∆²uvw on sequence space l1 is defined by ∆²uvw x= (unxn + vn−1 xn−1 + wn−2 xn−2) ∞ n=0 with x−1, x−2 = 0, where x = (xn) ∈l1 , u= (uk) is either constant or strictly increasing sequence of positive real numbers with U = lim k→∞ u k, v = (vk) is a sequence of real numbers such that vk ≠ 0 for each k∈N0 with V = lim k →∞ vk ≠ 0 and w = (wk) is a non-increasing sequence of positive real numbers such that wk ≠ 0 for each k∈N0 with W = lim k→∞ wk ≠ 0. In this paper we have obtained the results on spectrum and point spectrum for the operator ∆²uvw over sequence space l1. We have also obtained the results on continuous spectrum σc(∆²uvw, l1), residual spectrum σr(∆²uvw, l1) and fine spectrum of the operator ∆²uvw on sequence space l1.
Wydawca
Rocznik
Strony
593--609
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
Bibliografia
  • [1] A. M. Akhmedov, F. Basar, On the fine spectra of the difference operator △ over the sequence spaces lp, (1 ≤ p < ∞), Demonstratio Math. 39 (2006), 585–595.
  • [2] A. M. Akhmedov, F. Basar, The fine spectra of the difference operator △ over the sequence spaces bvp, (1 ≤ p < ∞), Acta Math. Sin. Eng. Ser. 23 (2007), 1757–1768.
  • [3] H. Bilgic, H. Furkan, On the fine spectrum of the operator B(r, s, t) over the sequence spaces l1 and bv, Math. Comput. Modelling 45 (2007), 883–891.
  • [4] H. Bilgic, H. Furkan, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces lp and bvp, (1 < p < ∞), Nonlinear Anal. 68 (2008), 499–506.
  • [5] J. P. Cartlidge, Weighted mean matrices as operators on lp, Ph. D Dissertation, Indiana University, 1978.
  • [6] H. Furkan, H. Bilgic, K. Kayaduman, On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces l1 and bv, Hokkaido Math. J. 35 (2006), 897–908.
  • [7] S. Goldberg, Unbounded Linear Operators, Dover Publications, Inc. New York, 1985.
  • [8] M. Gonzalez, The fine spectrum of the Cesaro operator in lp, (1 < p < ∞), Arch. Math. 44 (1985), 355–358.
  • [9] K. Kayaduman, H. Furkan, The fine spectra of the difference operator △ over the sequence space l1 and bv, Int. Math. Forum 1 (2006), 1153–1160.
  • [10] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, Inc. New York - Chichester - Brisbane - Toronto, 1978.
  • [11] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 1988.
  • [12] A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies, Amsterdam - New York - Oxford, 1984.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0035-0009
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