\Lambda(p)-sets and the limit order of operator ideals
泛函分析
2007-05-23 v1 经典分析与常微分方程
摘要
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.
引用
@article{arxiv.math/9904176,
title = {\Lambda(p)-sets and the limit order of operator ideals},
author = {Carsten Michels},
journal= {arXiv preprint arXiv:math/9904176},
year = {2007}
}
备注
6 pages