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On Minimal and Maximal p-operator Space Structures
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 166-177
- Print publication:
- 14 March 2014
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- Article
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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.
