Λ(p)-sets and the limit order of operator ideals

Details Λ(p)-sets and the limit order of operator ideals Λ(p)-sets and the limit order of operator ideals

1999-04-30

arxiv.org/abs/math/9904176v1

Mathematics

Functional Analysis

6 pages

Scientific paper

Given an infinite set \Lambda of characters on a compact abelian group we show that \Lambda is a \Lambda(p)-set for all p>2 if and only if the limit order of the ideal of all \Lambda-summing operators coincides with that of the ideal of all Gaussian-summing operators. This is a natural counterpart to a recent result of Baur which says that \Lambda is a Sidon set if and only if even the two operator ideals from above coincide. Furthermore, our techniques, which are mainly based on complex interpolation, lead us to exact asymptotic estimates of the Gaussian-summing norm of identities between finite-dimensional Schatten classes.

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