Absolutely p-summing operator
= Absolutely p-summing operator
{title2=$\pi_p(T)$}
= p-summing operator
{synonym}
For $1\le p<\infty$, a <bounded linear operator> $T:E\to F$ between <Banach spaces> is absolutely p-summing if $(\sum_j\|Tx_j\|^p)^{1/p}\le C\sup_{\phi\in B_{E^*}}(\sum_j|\phi(x_j)|^p)^{1/p}$ for every finite family. The least $C$ is its p-summing norm $\pi_p(T)$. Direct substitution gives the ideal inequality $\pi_p(BTA)\le\|B\|\pi_p(T)\|A\|$ for compatible <bounded linear operators>.