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DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES

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

  • [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.
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

Ramazan Kama

Bilal Altay

Publication Date October 15, 2017
Submission Date May 4, 2017
Acceptance Date May 17, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Kama, R., & Altay, B. (2017). DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp Journal of Mathematics, 5(2), 260-267.
AMA Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. October 2017;5(2):260-267.
Chicago Kama, Ramazan, and Bilal Altay. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics 5, no. 2 (October 2017): 260-67.
EndNote Kama R, Altay B (October 1, 2017) DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp Journal of Mathematics 5 2 260–267.
IEEE R. Kama and B. Altay, “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”, Konuralp J. Math., vol. 5, no. 2, pp. 260–267, 2017.
ISNAD Kama, Ramazan - Altay, Bilal. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics 5/2 (October 2017), 260-267.
JAMA Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. 2017;5:260–267.
MLA Kama, Ramazan and Bilal Altay. “DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES”. Konuralp Journal of Mathematics, vol. 5, no. 2, 2017, pp. 260-7.
Vancouver Kama R, Altay B. DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp J. Math. 2017;5(2):260-7.
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