LOCAL PROPERTIES OF THE HOCHSCHILD COHOMOLOGY OF C*-ALGEBRAS

Abstract

AbstractLet A be a C*-algebra, and let X be a Banach A-bimodule. Johnson [B. E. Johnson, ‘Local derivations on C*-algebras are derivations’, Trans. Amer. Math. Soc. 353 (2000), 313–325] showed that local derivations from A into X are derivations. We extend this concept of locality to the higher cohomology of a C*-algebra and show that, for every $n\in \mathbb {N}$, bounded local n-cocycles from A(n) into X are n-cocycles.