An Extension of the Spectral Mapping Theorem

Abstract EN

We give an extension of the spectral mapping theorem on hypergroups and prove that if K is a commutative strong hypergroup with K^=Xb(K) and κ is a weakly continuous representation of M(K) on a W∗-algebra such that for every t∈K, κt is an ∗-automorphism, spκ is a synthesis set for L1(K) and κ(L1(K)) is without order, then for any μ in a closed regular subalgebra of M(K) containing L1(K), σ(κ(μ))=μ^(spκ)¯, where spκ is the Arveson spectrum of κ.