EUDML

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Spaces of Lipschitz and Hölder functions and their applications.

Nigel J. Kalton — 2004

Collectanea Mathematica

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.

Nigel J. Kalton — 2008

Revista Matemática Complutense

Property (M), M-ideals, and almost isometric structure of Banach spaces.

Dirk Werner; Nigel J. Kalton — 1995

Journal für die reine und angewandte Mathematik

The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos; Nigel J. Kalton — 2001

Studia Mathematica

This article is concerned with the question of whether Marcinkiewicz multipliers on $ℝ^{2 n}$ 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

Yves Dutrieux; Nigel J. Kalton — 2005

Studia Mathematica

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

Kenneth J. Dykema; Nigel J. Kalton — 2005

Annales de l’institut Fourier

Let $ℳ$ be a factor of type II $_{\infty}$ or II $_{1}$ having separable predual and let $\bar{ℳ}$ be the algebra of affiliated $τ$ -measurable operators. We characterize the commutator space $[ℐ, 𝒥]$ for sub- $(ℳ, ℳ)$ - bimodules $ℐ$ and $𝒥$ of $\bar{ℳ}$ .

Marcos de traslaciones.

Peter G. Casazza; Ole Christensen; Nigel J. Kalton — 2001

Collectanea Mathematica

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