Gap-interpolation theorems for entire functions.
Convexity, type and three space problem
Multilinear Calderón-Zygmund operators on Hardy spaces.
It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.
Remarks on rich subspaces of Banach spaces
We investigate rich subspaces of L₁ and deduce an interpolation property of Sidon sets. We also present examples of rich separable subspaces of nonseparable Banach spaces and we study the Daugavet property of tensor products.
Embedding l -cubes in finite-dimensional 1-subsymmetric spaces.
Spaces of Lipschitz and Hölder functions and their applications.
We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if and only if...
The nonlinear geometry of Banach spaces.
Some Ramsey type theorems for normed and quasinormed spaces
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Property (M), M-ideals, and almost isometric structure of Banach spaces.
The Marcinkiewicz multiplier condition for bilinear operators
This article is concerned with the question of whether Marcinkiewicz multipliers on give rise to bilinear multipliers on ℝⁿ × ℝⁿ. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy spaces.
Perturbations of isometries between C(K)-spaces
We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L.
Sums of commutators in ideals and modules of type II factors
Let be a factor of type II or II having separable predual and let be the algebra of affiliated -measurable operators. We characterize the commutator space for sub-- bimodules and of .
Marcos de traslaciones.
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