On Lipschitz functions of subnormal operators

Abstract EN

We prove the following:Theorem: Let S be a subnormal operator on an infinite dimensional separable complex Hilbert space H.

Let f be analytic and Lipschitz on a neighborhood e of the spectrum σ(S) of S.

Then ||f(S)X-X f(S)||2 ≤ K||Sx-X S||2 for some K> O and for every X ε B(H), the algebra of all bounded linear operators on H, where ||.||2 is the Hilbert-Schmidt norm.

A.M.S.

subject classification number 1990: 47 B 20, 47 A 25.