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Journal of Function Spaces
Volume 2016, Article ID 4372471, 6 pages
http://dx.doi.org/10.1155/2016/4372471
Research Article

Mappings of Type Special Space of Sequences

1Department of Mathematics, Faculty of Science and Arts, University of Jeddah (UJ), P.O. Box 355, Khulais 21921, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, Egypt

Received 12 April 2016; Revised 26 June 2016; Accepted 28 July 2016

Academic Editor: Gianluca Vinti

Copyright © 2016 Awad A. Bakery. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give sufficient conditions on a special space of sequences defined by Mohamed and Bakery (2013) such that the finite rank operators are dense in the complete space of operators whose approximation numbers belong to this sequence space. Hence, under a few conditions, every compact operator would be approximated by finite rank operators. We apply it on the sequence space defined by Tripathy and Mahanta (2003). Our results match those known for -absolutely summable sequences of reals.