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The notions of column and row operator space were extended by A. Lambert fromHilbert spaces to general Banach spaces. In this paper, we use column and rowspaces over quotients of subspaces of general $L_p$-spaces to equip severalBanach algebras occurring naturally in abstract harmonic analysis withcanonical, yet not obvious operator space structures that turn them intocompletely bounded Banach algebras. We use these operator space structures togain new insights on those algebras.

Column and row operator spaces over QSL_p-spaces and their use in abstract harmonic analysis