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We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Z n (L 1 (G),X), the space of bounded n-cocycles from L 1 (G) (n) into X, where L 1 (G) is the group algebra of a locally compact group G and X is a Banach L 1 (G)-bimodule. We show that Z n (L 1 (G),X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almost periodic groups, and totally disconnected groups. If, in addition, G is amenable and X is the dual of an essential Banach L 1 (G)-bimodule, then we show that Z 1 (L 1 (G),X) satisfies a stronger property, namely hyperreflexivity. This, in particular, implies that Z 1 (L 1 (G),L 1 (G)) is hyperreflexive.

Reflexivity and hyperreflexivity of bounded 𝑁-cocycles from group algebras