On the normal spectrum of a subnormal operator

Abstract

In this note we present a new characterization for subnormality which is purely C ∗ {C^ \ast } -algebraic. We also establish an intrinsic characterization of the normal spectrum for a subnormal operator, which enables us to prove that σ ⊥ ( π ( S ) ) ⊆ σ ⊥ ( S ) {\sigma _ \bot }(\pi (S)) \subseteq {\sigma _ \bot }(S) for any ∗ ^ \ast -representation π \pi .