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Schauder bases and the bounded approximation property in separable Banach spaces

Jorge Mujica, Daniela M. Vieira (2010)

Studia Mathematica

Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 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 (Tₙ) of canonical projections in F has the properties s u p n | | T | | λ + ϵ and l i m s u p n | | T | | λ . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for L p -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.

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