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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

Country: Qatar, Subject Area: Mathematics

Pages: 981 - 988

Edition: Volume 8 Issue 5, May 2019

How to Cite this Article?

Shawgy Hussein, Nazar Bakri Musaad, "Application on Absolutely Summing Operators on a Tree Space and the Bounded Approximation Property", International Journal of Science and Research (IJSR), https://www.ijsr.net/archive/v8i5/show_abstract.php?id=ART20197781, Volume 8 Issue 5, May 2019, 981 - 988

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