Research Article
BibTex RIS Cite

On Vector-Valued Operator Riesz Sequence Spaces

Year 2019, Volume: 68 Issue: 1, 236 - 247, 01.02.2019
https://doi.org/10.31801/cfsuasmas.451537

Abstract

In this paper we introduce vector-valued Riesz sequence spaces R₀^{q}(X), R_{c}^{q}(X), R_{∞}^{q}(X) and R₁^{q}(X) and determine their Köthe-Toeplitz duals. Also, we characterize some matrix classes.

References

  • Lorentz, G. G. and Machphail, M. S., Unbounded operators and a theorem of A. Robinson, Trans. Royal Soc. of C XLVI, (1952), 33-37.
  • Robinson, A.R., On functional transformations and summability, Proc. London Math. Soc., 52, (1995), 132-160.
  • Maddox, I. J., Infinite matrices of operators, Lecture notes in Mathematics, 786 Springer-Verlag, Berlin.
  • Maddox, I. J., Spaces of strongly summable sequences, The Quarterly Journal of Mathematics, 18(1), (1967), 345-53.
  • Nappus, A. and Sõrmus, T., Einige verallgemeinerte matrixverfahren, Proc. Estonian Acad. Sci. Phys.Math., 45(2-3), (1996), 201-210.
  • Aasma, A., Matrix transformations of summability domains of generalized matrix methods in Banach spaces, Rendiconti del Circolo Matematico di Palermo, 58, (2009), 467-476 .
  • Malkowsky, E. and Rakočević, V., Measure of noncompactness of linear operators between spaces of sequences that are (N,q) summable or bounded, Czechoslovak Mathematical Journal, 51, (126), (2001), 505-522.
  • Şengönül, M. and Başar, F., Some new Cesàro sequence spaces of non-absolute type which include the spaces c₀ and c, Soochow Journal of Mathematics, 31(1), (2005), 107-119.
  • Altay, B. and Başar, F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 24(2), (2003), 701-715.
  • Altay, B. and Başar, F., Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 30(4), (2006), 591-608.
  • Altay, B. and Başar, F., Some Euler sequence spaces of non-absolute type, Ukrainian Mathematical Journal, 57(2), (2005), 1-17.
Year 2019, Volume: 68 Issue: 1, 236 - 247, 01.02.2019
https://doi.org/10.31801/cfsuasmas.451537

Abstract

References

  • Lorentz, G. G. and Machphail, M. S., Unbounded operators and a theorem of A. Robinson, Trans. Royal Soc. of C XLVI, (1952), 33-37.
  • Robinson, A.R., On functional transformations and summability, Proc. London Math. Soc., 52, (1995), 132-160.
  • Maddox, I. J., Infinite matrices of operators, Lecture notes in Mathematics, 786 Springer-Verlag, Berlin.
  • Maddox, I. J., Spaces of strongly summable sequences, The Quarterly Journal of Mathematics, 18(1), (1967), 345-53.
  • Nappus, A. and Sõrmus, T., Einige verallgemeinerte matrixverfahren, Proc. Estonian Acad. Sci. Phys.Math., 45(2-3), (1996), 201-210.
  • Aasma, A., Matrix transformations of summability domains of generalized matrix methods in Banach spaces, Rendiconti del Circolo Matematico di Palermo, 58, (2009), 467-476 .
  • Malkowsky, E. and Rakočević, V., Measure of noncompactness of linear operators between spaces of sequences that are (N,q) summable or bounded, Czechoslovak Mathematical Journal, 51, (126), (2001), 505-522.
  • Şengönül, M. and Başar, F., Some new Cesàro sequence spaces of non-absolute type which include the spaces c₀ and c, Soochow Journal of Mathematics, 31(1), (2005), 107-119.
  • Altay, B. and Başar, F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 24(2), (2003), 701-715.
  • Altay, B. and Başar, F., Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 30(4), (2006), 591-608.
  • Altay, B. and Başar, F., Some Euler sequence spaces of non-absolute type, Ukrainian Mathematical Journal, 57(2), (2005), 1-17.
There are 11 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Osman Duyar

Serkan Demiriz 0000-0002-4662-6020

Publication Date February 1, 2019
Submission Date August 4, 2017
Acceptance Date October 30, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Duyar, O., & Demiriz, S. (2019). On Vector-Valued Operator Riesz Sequence Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 236-247. https://doi.org/10.31801/cfsuasmas.451537
AMA Duyar O, Demiriz S. On Vector-Valued Operator Riesz Sequence Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):236-247. doi:10.31801/cfsuasmas.451537
Chicago Duyar, Osman, and Serkan Demiriz. “On Vector-Valued Operator Riesz Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 236-47. https://doi.org/10.31801/cfsuasmas.451537.
EndNote Duyar O, Demiriz S (February 1, 2019) On Vector-Valued Operator Riesz Sequence Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 236–247.
IEEE O. Duyar and S. Demiriz, “On Vector-Valued Operator Riesz Sequence Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 236–247, 2019, doi: 10.31801/cfsuasmas.451537.
ISNAD Duyar, Osman - Demiriz, Serkan. “On Vector-Valued Operator Riesz Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 236-247. https://doi.org/10.31801/cfsuasmas.451537.
JAMA Duyar O, Demiriz S. On Vector-Valued Operator Riesz Sequence Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:236–247.
MLA Duyar, Osman and Serkan Demiriz. “On Vector-Valued Operator Riesz Sequence Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 236-47, doi:10.31801/cfsuasmas.451537.
Vancouver Duyar O, Demiriz S. On Vector-Valued Operator Riesz Sequence Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):236-47.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.