Remarks on Hyponormal Operators and Almost Normal Operators
نویسنده
چکیده
In 1984 M. Putinar proved that hyponormal operators are subscalar 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 ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this sufficient condition amounts to in the case of a weighted shift operator.
منابع مشابه
Some Remarks about Almost Semi-hyponormal Operators
We define the class of almost semi-hyponormal operators on a Hilbert space and provide some sufficient conditions in which such operators are almost normal, that is their self-commutator is in the trace-class. Mathematics Subject Classification: 47B20
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