Schauder bases and the bounded approximation property in separable Banach spaces

Author(s)

Mujica, Jorge ^[1] ; Vieira, Daniela M. ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: STUDIA MATHEMATICA; v. 196, n. 1, p. 1-12, 2010.
• Web of Science Citations: 3

Abstract

Let E be a separable Banach space with the A-bounded approximation property. We show that for each epsilon > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (T(n)) of canonical projections in F has the properties sup(n is an element of N) parallel to T(n)parallel to <= lambda +is an element of and lim sup(n ->infinity) parallel to T(n)parallel to <= lambda This is a sharp quantitative version of a classical result obtained independently by Pelczynski and by Johnson, Rosenthal and Zippin. (AU)

• FAPESP's process: 06/02378-7 - Infinite Dimensional Analysis
• Grantee: Jorge Tulio Mujica Ascui
• Support Opportunities: Research Projects - Thematic Grants