International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Fully Refereed | Open Access | Double Blind Peer Reviewed

ISSN: 2319-7064


Downloads: 123 | Views: 184

Research Paper | Mathematics | Qatar | Volume 8 Issue 5, May 2019


Application on Absolutely Summing Operators on a Tree Space and the Bounded Approximation Property

Shawgy Hussein | Nazar Bakri Musaad


Abstract: For describing the space P (C [0, 1], X), where X is a Banach space, of absolutely summing operators from C [0, 1] to X in terms of the space X itself, we construct a tree space l_1^tree (X) on X. It consists of special trees in X which we call two-trunk trees. We show that P (C [0, 1], X) is isometrically isomorphic to l_1^tree (X). As an application on [19], we characterize the bounded approximation property (BAP) and the weak BAP in terms of X^*-valued square sequence spaces.


Keywords: Banach spaces, Absolutely summing operators, Two-trunk trees, Linear B-splines, Continuous functions on 0, 1, Bounded approximation properties


Edition: Volume 8 Issue 5, May 2019,


Pages: 981 - 988


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