Remarks on hyponormal operators and almost normal operators.
Abstract
In 1984 M. Putinar proved that hyponormal operators are sub-scalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S, so that T\oplus S is the sum of a normal operator and a Hilbert-Schmidt operator. We will investigate what this sufficient condition amounts to in the case of a weighted shift operator.The authors retain all rights to the original work without any restrictions.
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