Complex Homomorphisms of the Algebras of Holomorphic Functions on Fréchet Spaces.
Spectra of Algebras of Holomorphic Functions on Infinite Dimensional Riemann Domains.
The Oka-Weil theorem in locally convex spaces with the approximation property
Spaces of holomorphic mappings on Banach spaces with a Schauder basis
We show that if U is a balanced open subset of a separable Banach space with the bounded approximation property, then the space ℋ(U) of all holomorphic functions on U, with the Nachbin compact-ported topology, is always bornological.
Holomorphic approximation in infinite-dimensional Riemann domains
Quotients with a shrinking basis
We present a simple proof of a theorem that yields as a corollary a result of Valdivia that sharpens an old result of Johnson and Rosenthal.
Mittag-Leffler methods in analysis.
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.
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
We present simple proofs that spaces of homogeneous polynomials on and 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
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 and . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.
Embeddings of Fréchet spaces in uniform Fréchet algebras
Extension of multilinear mappings on Banach spaces
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