Displaying similar documents to “Interpolation sets for Fréchet measures”

Hausdorff Measures of Noncompactness and Interpolation Spaces

da Silva, Eduardo Brandani, Fernanadez, Dicesar L. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B50, 46B70, 46G12. A new measure of noncompactness on Banach spaces is defined from the Hausdorff measure of noncompactness, giving a quantitative version of a classical result by R. S. Phillips. From the main result, classical results are obtained now as corollaries and we have an application to interpolation theory of Banach spaces.

Interpolation between H spaces and non-commutative generalizations (II).

Gilles Pisier (1993)

Revista Matemática Iberoamericana

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We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can...

Characterizing Sidon sets by interpolation properties of subsets

Colin C. Graham, Kathryn E. Hare (2008)

Colloquium Mathematicae

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Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups...

ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures

Colin C. Graham, Kathryn E. Hare (2006)

Studia Mathematica

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A subset E of a discrete abelian group is a "Fatou-Zygmund interpolation set" (FZI₀ set) if every bounded Hermitian function on E is the restriction of the Fourier-Stieltjes transform of a discrete, non-negative measure. We show that every infinite subset of a discrete abelian group contains an FZI₀ set of the same cardinality (if the group is torsion free, a stronger interpolation property holds) and that ε-Kronecker sets are FZI₀ (with that stronger interpolation...

On interpolation of tensor products of Banach spaces.

Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)

RACSAM

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For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.

Interpolation of the measure of non-compactness by the real method

Fernando Cobos, Pedro Fernández-Martínez, Antón Martínez (1999)

Studia Mathematica

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We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.