Displaying similar documents to “On Sparr and Fernandez's interpolation methods of Banach spaces.”

Interpolation of the measure of non-compactness between quasi-Banach spaces.

Pedro Fernández Martínez (2006)

Revista Matemática Complutense

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We study the behavior of the ball measure of non-compactness under several interpolation methods. First we deal with methods that interpolate couples of spaces, and then we proceed to extend the results to methods that interpolate finite families of spaces. We will need an approximation hypothesis on the target family of spaces.

On vector-valued inequalities for Sidon sets and sets of interpolation

N. Kalton (1993)

Colloquium Mathematicae

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Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to L p -norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation ( I 0 -set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus...