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On Minimal and Maximal p-operator Space Structures
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that ${{L}^{\infty }}\left( \mu \right)$, in its capacity as multiplication operators on ${{L}^{p}}\left( \mu \right)$, is minimal as a $p$-operator space for a decomposable measure $\mu $. We conclude that ${{L}^{1}}\left( \mu \right)$ has a certain maximal type $p$-operator space structure that facilitates computations with ${{L}^{1}}\left( \mu \right)$ and the projective tensor product.
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- Copyright © Canadian Mathematical Society 2014