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Mittag-Leffler methods in analysis.

Jorge Mújica — 1995

Revista Matemática de la Universidad Complutense de Madrid

In this survey we present two Mittag-Leffler lemmas and several applications to topics as varied as the delta-equation, Fréchet algebras, inductive limits of Banach spaces and quasi-normable Fréchet spaces.

Separable quotients of Banach spaces.

Jorge Mújica — 1997

Revista Matemática de la Universidad Complutense de Madrid

In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Banach spaces of homogeneous polynomials without the approximation property

Seán DineenJorge Mujica — 2015

Czechoslovak Mathematical Journal

We present simple proofs that spaces of homogeneous polynomials on L p [ 0 , 1 ] and p provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).

Schauder bases and the bounded approximation property in separable Banach spaces

Jorge MujicaDaniela 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.

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