The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general Lp-spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banach algebras. We use these operator space structures to gain new insights on those algebras.

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Journal of Mathematical Analysis and Applications
School of Mathematics and Statistics

Neufang, M, & Runde, V. (Volker). (2009). Column and row operator spaces over QSLp-spaces and their use in abstract harmonic analysis. Journal of Mathematical Analysis and Applications, 349(1), 21–29. doi:10.1016/j.jmaa.2008.08.021