Remarks on hyponormal operators and almost normal operators.

  • Vasile Lauric Florida A&M University
Keywords: Hilbert-Schmidt and trace-class operators, hyponormal operators, almost normal operators


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.

Author Biography

Vasile Lauric, Florida A&M University

Department of Mathematics