Minimal and maximal $p$-operator space structures

Serap Oztop, Nico Spronk

Published 2011-12-20, updated 2012-07-11Version 3

We show that $L^\infty(\mu)$, in its capacity as multiplication operators on $L^p(\mu)$, is minimal as a $p$-operator space for a decomposable measure $\mu$. We conclude that $L^1(\mu)$ has a certain maximal type $p$-operator space structure which facilitates computations with $L^1(\mu)$ and the projective tensor product.