(Almost) C*-algebras as sheaves with self-action
(Almost) C*-algebras as sheaves with self-action
Via Gelfand duality, a unital C*-algebra A induces a functor from compact Hausdorff spaces to sets, \mathsf{CHaus}\to\mathsf{Set} . We show how this functor encodes standard functional calculus in A as well as its multivariate generalization. Certain sheaf conditions satisfied by this functor provide a further generalization of functional calculus. Considering …