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On Minimal and Maximal p-operator Space Structures

Published online by Cambridge University Press:  20 November 2018

Serap Öztop  and
Nico Spronk
Serap Öztop
Affiliation:
Istanbul University, Faculty of Science, Department of Mathematics, 34134 Vezneciler, Istanbul, Turkey e-mail: oztops@istanbul.edu.tr
Nico Spronk
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 e-mail: nspronk@uwaterloo.ca
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Abstract

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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.

Keywords

46L0747L2546G10p-operator spacemin spacemax space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 166 - 177
Copyright
Copyright © Canadian Mathematical Society 2014

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