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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 212957, 8 pages
http://dx.doi.org/10.1155/2012/212957
Research Article

A New Class of Banach Spaces and Its Relation with Some Geometric Properties of Banach Spaces

Department of Mathematics, Yazd University, Yazd 89195-741, Iran

Received 29 December 2011; Accepted 14 February 2012

Academic Editor: Saminathan Ponnusamy

Copyright © 2012 M. Salimi and S. M. Moshtaghioun. 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

By introducing the concept of L-limited sets and then L-limited Banach spaces, we obtain some characterizations of it with respect to some well-known geometric properties of Banach spaces, such as Grothendieck property, Gelfand-Phillips property, and reciprocal Dunford-Pettis property. Some complementability of operators on such Banach spaces are also investigated.