Abstract. In this note we obtain some sufficient conditions that a trace-class commutator have trace zero, and we use these results together with two theorems of Voiculescu to establish some structure theorems for hyponormal-like operators and to give short proofs of theorems of G. Weiss and Helton--Howe.

AMS Subject Classification (1991): 47B20

Keyword(s): Commutators, trace zero, almost hyponormal operators

Received June 22, 1999. (Registered under 2738/2009.)