On Hilbert \(I\)-convergent sequence spaces

Volume 20, Issue 3, pp 225--233 http://dx.doi.org/10.22436/jmcs.020.03.05
Publication Date: December 11, 2019 Submission Date: April 16, 2019 Revision Date: October 11, 2019 Accteptance Date: October 31, 2019

Authors

Vakeel A. Khan - Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India. Kamal M. A. S. Alshlool - Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India. Masood Alam - Department of Mathematics and IT Center for Preparatory Studies, Sultan Qaboos University, P. O. Box 162-PC, 123 Al Khoud Muscat, Sultanate of Oman.


Abstract

In this paper, we define some new sequence spaces \(c^{I}_{0}(H)\), \(c^{I}(H)\), \(\ell^{I}_{\infty}(H)\), and \(\ell_{\infty}(H)\) as a domain of triangle Hilbert matrix and study some topological and algebraic properties of these spaces. Further, we study some inclusion relations concerning these spaces.


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