On the Zweier sequence space

• Autorzy: Sengonul M.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to introduce the Zweier sequence spaces Ż and Ż0 consisting of all sequences x = (xk) such that (Zx) in the space c and c0 respectively, which is normed. Also, prove that Ż and Ż0 are linearly isomorphic to the space c and c0 respectively. Additionally, the alpha, beta and gamma -duals of the spaces Ż and Ż0 have been computed and space of Ż0 Schauder base have been constructed. Furthermore, given the two theorem concerning matrix map. Finally, the norm of Zweier operator have been given and the .ne spectrum of the Zweier operator over the sequence spaces c and c0 has been determined.

Słowa kluczowe

EN

sequence spaces; Banach space; Zweir space; matrix tranformations; isomorphism; spectrum

PL

przestrzeń ciągu; przestrzeń Banacha; przestrzeń Zweira; odwzorowanie macierzowe; izomorfizm; widmo

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 1
• Strony: 181--196
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Sengonul M.

• Malatya Bilim ve Sanat Merkezi 44000 Malatya, Turkiye,

Bibliografia

• [1] M. Ali Akhmedov and F. Basar, The fine spectra of the difference operator over the sequence space lp, (1? p < ?), (under comminication).
• [2] B. Altay, F. Başar and Mursaleen, On the Euler sequence spaces which include the spaces lp and l? I, (under comminication).
• [3] B. Altay and F. Başar, The fine spectra of the difference operator over the sequence space on c0 and c, Uniform Sci., (in press).
• [4] F. Basar and B. Altay, On the spaces of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (2003), (to appear).
• [5] F. Basar, Matrix transformations between certain sequence spaces of Xp and lp, Soochow J. Math. 26 (2000), no. 2, 191–204.
• [6] F. Başar and R. Colak, Almost-conversative matrix transformations, Doga Math. 13 (3) (1989), 91–100.
• [7] J. Boos, Classical and Modern Methods in Summability, Oxford University Press, 2000.
• [8] B. Cohuldhary and S. Nanda, Functional Analysis with Applications, John Wiley & Sons Inc. New Delhi. 1989.
• [9] S. Goldberg, Weighed Linear Operator, Dover Publications Inc., New York, 1966–1978.
• [10] E. Kreyszig, Introductory Functional Analysis with Applications, JohnWiley & Sons Inc. New York-Chichester-Brisbane-Toronto, 1978.
• [11] B. Kuttner, On dual summability methods, Proc. Comb. Phil. Soc. 71 (1972), 67–73.
• [12] G. G. Lorentz, Über Limitieurngsverfahahren die von einem Stieltjes-Integral abhangen, Acta Math. 79 (1947), 255–272.
• [13] G. G. Lorentz and K. Zeller, Summation of sequences and summation of series, Proc. Camb. Phil. Soc. 71 (1972), 67–73.
• [14] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 2nd ed., 1988.
• [15] E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mat. Vesnik 49 (1997), 187–196.
• [16] P.-N. Ng, P.-Y. Lee, Cesaro sequence spaces of non-absolute type, Comment. Math. Prace Mat. 20 (2) (1978), 429–433.
• [17] J. T. Okutoyi, On the sepectrum C1 as an operator on bv, Commun Fac. Sci Univ. Ank. Ser. A1 41 (1992), 197–207.
• [18] C. Orhan and E. Öztürk, On f-regular dual summability methods, Bull. Inst. Math. Acad. Sinica 14 (1) (1986), 99–104.
• [19] J. B. Reade, On the spectrum of Cesaro operator, Bull. Lond. Math. Soc. 17 (1985), 263–267.
• [20] M. Stieglitz, H. Tietz, Matrix transformationen von folgenraumen eine ergebnisbersicht, Math. Z. 154 (1977), 1–16.
• [21] M. Şengönül and F. Başar, Some new Cesaro sequence spaces on non-absolute type which include the spaces c0 and c, Soochow J. Math. 31 (2005), 107–119.
• [22] C.-S. Wang, On Nörlund sequence spaces, Tamkang J. Math. 9 (1978), 269–274.
• [23] A. Wilansky, Summability through Functional Analysis, Nort-Holland, Mathematics Studies, 85, Amsterdam-New York-Oxford, 1984.
• [24] M. Yildirim, On the spectrum and fine spectrum of the compact Rhally operators, Indian J. Pure Appl. Math. 27 (8) (1996), 779–784.