The Bessaga-Pelczynski Property and Strongly Bounded Measures
The best constants in the Khintchine inequality
The chain rule for differentiable measures
The dual form of the approximation property for a Banach space and a subspace
Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. In particular, if the pair (X,Y) has the AP then X, Y, and the quotient space X/Y have the classical Grothendieck AP. The main result is an easy to apply dual formulation of this property. Applications...
The existence in every separable Banach space of a fundamental total and bounded biorthogonal sequence and related constructions of uniformly bounded orthonormal systems in
The Laplace transform of measures on the cone of a vector lattice.
The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition
It is proved that the Levi problem for certain locally convex Hausdorff spaces over with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies...
The Moment Problem in the Space C... (S).
The One-Third-Trick and Shift Operators
We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.
The Point of Continuity Property: Descriptive Complexity and Ordinal Index
∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Let X be a separable Banach space without the Point of Continuity Property. When the set of closed subsets of its closed unit ball is equipped with the standard Effros-Borel structure, the set of those which have the Point of Continuity Property is non-Borel. We also prove that, for any separable Banach space X, the oscillation rank of the identity on X (an ordinal index which quantifies the Point of Continuity Property) is determined by the subspaces...
The space of all bounded operators on Hilbert space does not have the approximation property
The Space of Differences of Convex Functions on [0, 1]
∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1]
The stability of bases in Banach and Hilbert spaces.
The uncomplemented subspace K(E,F)
The unit ball of every infinite-dimensional normed linear space contains a (1+ɛ)-separated sequence
The use of operators for the construction of normal bases for the space of continuous functions on .
The van der Put base for -functions.
The wavelet type systems
We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
The weak distance between Banach spaces with a symmetric basis.
Three-space problems and bounded approximation properties
Let be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an -space, then both X and A have bases. We apply these results to show that the spaces and have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.