Absolutely summing linear operators into spaces with no finite cotype

Details Absolutely summing linear operators into spaces with no finite cotype Absolutely summing linear operators into spaces with no finite cotype

2008-01-14

arxiv.org/abs/0801.2051v1

Mathematics

Functional Analysis

7 pages

Scientific paper

Given an infinite-dimensional Banach space $X$ and a Banach space $Y$ with no finite cotype, we determine whether or not every continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing for almost all choices of $p$ and $q$, including the case $p=q$. If $X$ assumes its cotype, the problem is solved for all choices of $p$ and $q$. Applications to the theory of dominated multilinear mappings are also provided.

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