Operators that admit a moment sequence

Abstract

We consider the question of which operators on Hilbert space admit a moment sequence, and show, in particular, that if T is any operator in ℒ(ℋ) that can be written as T = N + K, where N is normal and K is compact, and ℳ ⊂ ℋ is any invariant subspace for T, then the restriction T|ℳ admits such a sequence.