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

How to Cite?: Shawgy Hussein, Nazar Bakri Musaad, "Application on Absolutely Summing Operators on a Tree Space and the Bounded Approximation Property", Volume 8 Issue 5, May 2019, International Journal of Science and Research (IJSR), Pages: 981-988, https://www.ijsr.net/getabstract.php?paperid=ART20197781, DOI: https://dx.doi.org/10.21275/ART20197781

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