Some Properties of a Regular Sequence in Hilbert Space.
Some properties of basic sequences in Banach spaces.
Some remarks on non-separable Banach spaces with Markuševič basis
Some remarks on symmetric basic sequences in L1
Some results about absolute summability of operators in Banach spaces.
In order to study the absolute summability of an operator T we consider the set ST = {{xn} | ∑||Txn|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if ST contains an orthonormal basis and it is natural to ask under which conditions two orthonormal basis define the same left ideal of nuclear operators. Using results about ST we solve this problem in the more general context of Banach spaces.
Some results on Banach spaces without local unconditional structure
Sous-espaces complémentés isomorphes à c... dans les produits tensoriels de Saphar.
Sous-espaces complémentés dans un espace à base inconditionnelle, d’après L. Tzafriri
Sous-espaces symétriques des espaces d'Orlicz
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.
Spline bases in classical function spaces on compact manifolds, Part II
Spline bases in classical function spaces on compact manifolds, Part I
Spline characterizations of H¹
Spreading basic sequences and subspaces of James' quasi-reflexive space.
Spreading sequences in JT
We prove that a normalized non-weakly null basic sequence in the James tree space JT admits a subsequence which is equivalent to the summing basis for the James space J. Consequently, every normalized basic sequence admits a spreading subsequence which is either equivalent to the unit vector basis of or to the summing basis for J.
Stability in Banach spaces.
Stochastic approximation properties in Banach spaces
We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an space into X whose range has probability one, then X is a quotient of an space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for...
Subspaces of which do not contain -isomorphically
Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure
It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
Subspaces of the Bourgain-Delbaen space
It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space has a subspace isomorphic to some .