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.
"A New Class of Banach Spaces and Its Relation with Some Geometric Properties of Banach Spaces." Abstr. Appl. Anal. 2012 (SI13) 1 - 8, 2012. https://doi.org/10.1155/2012/212957