Column and row operator spaces-which we denote by COL and ROW; respectively-over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p; p 0 Að1; NÞ with 1 p þ 1 p 0 ¼ 1; we use the operator space structure on CBðCOLðL p 0 ðGÞÞÞ to equip the Figa`-Talamanca-Herz algebra A p ðGÞ with an operator space structure, turning it into a quantized Banach algebra. Moreover, we show that, for ppqp2 or 2pqpp and amenable G; the canonical inclusion A q ðGÞCA p ðGÞ is completely bounded (with cb-norm at most K 2

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