Some New Hilbert Sequence Spaces
The main purpose of the present paper is to study of some new Hilbert sequence spaces , and . New Hilbert sequence spaces , and consisting all the sequences whose - transforms are in the spaces , and , respectively. The new Hilbert sequence spaces , and that are - spaces and prove that the spaces , and are linearly isomorphic to the spaces , and , respectively. Afterward the bases and α, β and γ duals of these spaces will be given. Finally, matrix the classes and have been characterized.
Anahtar Kelimeler:
Hilbert sequence spaces, α, β and γ duals and bases of sequence, Matrix mappings
Some New Hilbert Sequence Spaces
The main purpose of the present paper is to study of some new Hilbert sequence spaces , and . New Hilbert sequence spaces , and consisting all the sequences whose - transforms are in the spaces , and , respectively. The new Hilbert sequence spaces , and that are - spaces and prove that the spaces , and are linearly isomorphic to the spaces , and , respectively. Afterward the bases and α, β and γ duals of these spaces will be given. Finally, matrix the classes and have been characterized.
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- [1] Choudhary, B., Nanda, S. Functional analysis with applications. Wiley, 1989.
- [2] Kırıscı, M. On The Taylor Sequence Spaces Of Nonabsolute Type Whıch Include The Spaces c0 AND c, Journal of Mathematical Analisys, 2, 22-35,2015.
- [3] Altay, B., Basar, F. On some Euler sequence spaces of nonabsolute type. Ukrainian Mathematical Journal, 57(1), 1-17, 2005.
- [4] Sengonül, M., Basar, F. Some new cesaro sequence spaces of non-absolute type which include. Soochow Journal of Mathematics, 31(1), 107-119, 2005.
- [5] Altay, B., Başar, F., Mursaleen, M. On the Euler sequence spaces which include in the spaces and ∞ I. Information Sciences, 176(10), 1450-1462, 2006.
- [6] Malkowsky, E. Recent results in the theory of matrix transformations in sequences spaces, Mat. Vesnik 49, 187-196, 1997
- [7] Ng, P. N., Lee, P. Y. Cesaro sequence spaces of non-absolute type. Comment. Math. Prace Mat, 20(2), 429-433, 1978
- [8] Wang, C. S. On Nörlund seqence spaces, Tamkang J. Math., 9, 269-274, 1978.
- [9] Raja, P. V. K., Chakravarthy, A. S. N., Avadhani, P. S. A Cryptosystem Based on Hilbert Matrix using Cipher Block Chaining Mode. arXiv preprint arXiv:1110.1498, 2011.
- [10] Tabanjeh, M. M. New Approach for the Inversion of Structured Matrices via Newton's Iteration, Advances in Linear Algebra and Matrix Theory, 5,(1) 1-15,2015.
- [11] Maddox, I. J. Elements of Functional Analysis, Cambridge University Press, Cambridge 1988.
- [12] Garling, D. J. H. The β-and γ-duality of sequence spaces. In Mathematical Proceedings of the Cambridge Philosophical Society, 63(4), 963-981, 1967
- [13] Stieglitz, M., Tietz, H. Matrixtransformationen von folgenräumen eine ergebnisübersicht. Mathematische Zeitschrift, 154(1), 1-16, 1977
- ISSN: 2147-7930
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2013
- Yayıncı: Muş Alparslan Üniversitesi