Research Article
Year 2017,
Volume: 5 Issue: 2, 260 - 267, 15.10.2017
Abstract
In this paper we show that completeness and barrelledness of a normed space can be characterized by means of sequence spaces obtained by a sequence in a normed space and difference matrix method. Other related results are established.
References
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- [2] Aizpuru, A. and Perez-Fernandez, F. J., Sequence spaces associated to a series in a Banach space (sequence spaces associated to a series), Indian J. pure appl. Math., 33 (2002), No. 9, 1317–1329.
- [3] F.Albiac, N. J.Kalton, Topics in Banach Spaces Theory, Springer-Verlag, New York (2006).
- [4] B. Altay, F. Basar Certain topological properties and duals of the domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), no. 2, 632–645.
- [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh., 55(1) (2003), 108–118; reprinted in Ukrainian Math. J., 55(1) (2003), 136–147.
- [6] C.A. Bektas, R. Colak, On some generalized difference sequence spaces, Thai J. Math., 3(1) (2005), 83–98.
- [7] C. Bessaga, A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Stud. Math., 17 (1958), 151–164.
- [8] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984).
- [9] M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math., 21(4) (1995), 377–386.
- [10] R. Kama, B. Altay, F. Basar, On the domains of backward difference matrix and the spaces of convergence of a series, preprint.
- [11] R. Kama, B. Altay, Some sequence spaces and completeness of normed spaces, Creat. Math. Inform., to appear.
- [12] V. Karakaya, E. Sava ̧s, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Mathematica Slovaca, 63(4) (2013), 849–862.
- [13] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169–175.
- [14] E. Malkowsky, Mursaleen and Qamaruddin, Generalized sets of difference sequences, their duals and matrix transformations, Advances in Sequence Spaces and Applications, Narosa, New Delhi, (1999), 68-83.
- [15] C.W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canad. J. Math., 8 (1956), 192–197.
- [16] F.J. Perez-Fernandez, F. Benıtez-Trujillo, A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J., 50 (2000), no. 125, 889–896.
Year 2017,
Volume: 5 Issue: 2, 260 - 267, 15.10.2017
Abstract
References
- [1] Aizpuru, A. and Perez-Fernandez, F. J., Characterizations of series in Banach spaces, Acta Math. Univ. Comenian., 58 (1999), No. 2, 337–344.
- [2] Aizpuru, A. and Perez-Fernandez, F. J., Sequence spaces associated to a series in a Banach space (sequence spaces associated to a series), Indian J. pure appl. Math., 33 (2002), No. 9, 1317–1329.
- [3] F.Albiac, N. J.Kalton, Topics in Banach Spaces Theory, Springer-Verlag, New York (2006).
- [4] B. Altay, F. Basar Certain topological properties and duals of the domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), no. 2, 632–645.
- [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh., 55(1) (2003), 108–118; reprinted in Ukrainian Math. J., 55(1) (2003), 136–147.
- [6] C.A. Bektas, R. Colak, On some generalized difference sequence spaces, Thai J. Math., 3(1) (2005), 83–98.
- [7] C. Bessaga, A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Stud. Math., 17 (1958), 151–164.
- [8] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984).
- [9] M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math., 21(4) (1995), 377–386.
- [10] R. Kama, B. Altay, F. Basar, On the domains of backward difference matrix and the spaces of convergence of a series, preprint.
- [11] R. Kama, B. Altay, Some sequence spaces and completeness of normed spaces, Creat. Math. Inform., to appear.
- [12] V. Karakaya, E. Sava ̧s, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Mathematica Slovaca, 63(4) (2013), 849–862.
- [13] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169–175.
- [14] E. Malkowsky, Mursaleen and Qamaruddin, Generalized sets of difference sequences, their duals and matrix transformations, Advances in Sequence Spaces and Applications, Narosa, New Delhi, (1999), 68-83.
- [15] C.W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canad. J. Math., 8 (1956), 192–197.
- [16] F.J. Perez-Fernandez, F. Benıtez-Trujillo, A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J., 50 (2000), no. 125, 889–896.
There are 16 citations in total.
Details
| Subjects | Engineering |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | October 15, 2017 |
| Submission Date | May 4, 2017 |
| Acceptance Date | May 17, 2017 |
| Published in Issue | Year 2017 Volume: 5 Issue: 2 |
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