On some Zweier convergent vector valued multiplier spaces

Year 2019, , 541 - 548, 01.08.2019

Ramazan Kama

https://doi.org/10.16984/saufenbilder.492788

Cited By: 1

Abstract

In this
paper, we introduce the Zweier convergent vector valued multiplier spaces M^\infty_Z(\sum_iT_ix_i)



















and M^\infty_wZ(\sum_iT_ix_i). We examine some topological
properties and some inclusion relations of these spaces.

Keywords

Vector valued multiplier space, Zweier matrix, summing operator, operator valued series

References

• A. Aizpuru, C. Pérez-Eslava, and J. B. Seoane Sepúlveda, “Matrix summability methods and weakly unconditionally Cauchy series,” The Rocky Mountain Journal of Mathematics, vol. 39, no. 2, pp. 367-380, 2009.
• F. Albiac and N. J. Kalton, “Topics in Banach Spaces Theory,” New York, Springer-Verlag, 2006.
• B. Altay and R. Kama, “On Cesàro summability of vector valued multiplier spaces and operator valued series,” Positivity, vol. 22, no. 2, pp. 575-586, 2018.
• F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers, İstanbul, 2012.
• F. Başar and B. Altay, “On the space of sequences of p-bounded variation and related matrix mappings”, (English, Ukrainian summary) Ukrain. Mat. Zh., vol. 55, no. 1, pp. 108-118, 2003; reprinted in Ukrainian Math. J., vol. 55, no. 1, pp. 136-14, 2003.
• J. Boos and P. Cass, “Classical and Modern Methods in Summability,” Oxford University Press, Oxford, 2000.
• J. Diestel, “Sequences and Series in Banach Spaces,” New York, Springer-Verlag, 1984.
• B. Hazarika, T. Karan, and B. K. Singh, “Zweier Ideal convergent sequence space defined by Orlicz function,” Journal of mathematics and computer science, vol. 8, no. 3, pp. 307-318, 2014.
• V. A. Khan, K. Ebadullah, A. Esi, and M. Shafiq, “On some Zweier I-convergent sequence spaces defined by a modulus function,” Afrika Matematika, vol. 26, no. 1-2, pp. 115-125, 2015.
• V. A. Khan and N. Khan, “Zweier I-Convergent Double Sequence Spaces Defined by a Sequence of Moduli,” Theory and Applications of Mathematics and Computer Science, vol. 5, no. 2, pp. 194-202, 2015.
• M. Mursaleen, “Applied Summability Methods, Springer Briefs,” Heidelberg New York Dordrecht London, 2014.
• F. J. Pérez-Fernández, F. Benítez-Trujillo, and A. Aizpuru, “Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series,” Czechoslovak Math. J., vol. 50, no. 4, pp. 889-896, 2000.
• C. Swartz, “Multiplier Convergent Series,” Singapore, World Sci. Publ., 2009.
• C. Swartz, “Operator valued series and vector valued multiplier spaces,” Casp. J. Math. Sci., vol. 3, no. 2, pp. 277-288, 2014.
• M. Şengönül, “On the Zweier sequence space,” Demonstratio Mathematica, vol. 40, no. 1, pp. 181-196, 2007.