Hyperreflexivity of bounded N-cocycle spaces of banach algebras

Let and be Banach spaces, , and the space of bounded -linear maps from (-times) into . The concept of hyperreflexivity has already been defined for subspaces of , where and are Banach spaces. We extend this concept to the subspaces of , taking into account its -linear structure. We then investigate when , the space of all bounded -cocycles from a Banach algebra into a Banach -bimodule , is hyperreflexive. Our approach is based on defining two notions related to a Banach algebra, namely the strong property and bounded local units, and then applying them to find uniform criterions under which is hyperreflexive. We also demonstrate that these criterions are satisfied in variety of examples including large classes of C-algebras and group algebras and thereby providing various examples of hyperreflexive -cocyle spaces. One advantage of our approach is that not only we obtain the hyperreflexivity for bounded -cocycle spaces in different cases but also our results generalize the earlier ones on the hyperreflexivity of bounded derivation spaces, i.e. when , in the literature. Finally, we investigate the hereditary properties of the strong property and b.l.u. This allows us to come with more examples of bounded -cocycle spaces which are hyperreflexive.