HYPERREFLEXIVITY CONSTANTS OF THE BOUNDED N-COCYCLE SPACES OF GROUP ALGEBRAS AND C*-ALGEBRAS

We introduce the concept of strong property (B) with a constant for Banach algebras and, by applying a certain analysis on the Fourier algebra of the unit circle, we show that all C*-algebras and group algebras have the strong property (B) with a constant given by 288 pi(1 + root 2). We then use this result to find a concrete upper bound for the hyperreflexivity constant of Z(n)(A, X), the space of bounded n-cocycles from A into X, where A is a C*-algebra or the group algebra of a group with an open subgroup of polynomial growth and X is a Banach A-bimodule for which Hn+1(A, X) is a Banach space. As another application, we show that for a locally compact amenable group G and 1 < p < infinity, the space CVp(G) of convolution operators on L-p(G) is hyperreflexive with a constant given by 384 pi(2)(1 + root 2). This is the generalization of a well-known result of Christensen ['Extensions of derivations. II', Math. Scand. 50(1) (1982), 111-122] for p = 2.