On Minimal and Maximal p-operator Space Structures

Öztop, Serap ; Spronk, Nico

Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 166-177

Résumé

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.

Détail

DOI : 10.4153/CMB-2012-030-7

Mots-clés : 46L07, 47L25, 46G10, p-operator space, min space, max space

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