Schauder bases and best approximation
Schauder bases and reflexivity
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.
Schauder bases in an abstract setting.
Schauder decompositions and multiplier theorems
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 -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.
Second derivatives of norms and contractive complementation in vector-valued spaces
We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces , where X is a Banach space with a 1-unconditional basis and p ∈ (1,2) ∪ (2,∞). If the norm of X is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection is then...
Selecting basic sequences in φ-stable Banach spaces
In this paper we make use of a new concept of φ-stability for Banach spaces, where φ is a function. If a Banach space X and the function φ satisfy some natural conditions, then X is saturated with subspaces that are φ-stable (cf. Lemma 2.1 and Corollary 7.8). In a φ-stable Banach space one can easily construct basic sequences which have a property P(φ) defined in terms of φ (cf. Theorem 4.5). This leads us, for appropriate functions φ, to new results on the existence of unconditional...
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.
Séries de Fourier et séries d'ondelettes
Simultaneous automorphisms on the space of analytic functions of several complex variables
Simultaneous resolutions of the identity operator in normed spaces.
We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.
Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces
Smooth partitions of unity on some non-separable Banach spaces
Sobre sumabilidad Cesáro en el espacio CS (I).
Some applications of p-summing operators to Banach space theory
Some geometric properties of finite dimensional, symmetric Banach spaces
Some linear topological properties of the spaces of operators on Hilbert space
Some new Properties of Sequence Spaces and Application to the Continued Fractions
Some notes on Markuševič bases in weakly compactly generated Banach spaces
Some problems arising in connection with the theory of vector measures