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.)
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