A BERBERIAN TYPE EXTENSION OF FUGLEDE-PUTNAM THEOREM FOR QUASI-CLASS A OPERATORS

  • Kim, In Hyoun (Department of Mathematics University of Incheon) ;
  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
  • Received : 2008.11.25
  • Published : 2008.12.01

Abstract

Let $\mathfrak{L(H)}$ denote the algebra of bounded linear operators on a separable infinite dimensional complex Hilbert space $\mathfrak{H}$. We say that $T{\in}\mathfrak{L(H)}$ is a quasi-class A operator if $$T^*{\mid}T^2{\mid}T{{\geq}}T^*{\mid}T{\mid}^2T$$. In this paper we prove that if A and B are quasi-class A operators, and $B^*$ is invertible, then for a Hilbert-Schmidt operator X $$AX=XB\;implies\;A^*X=XB^*$$.

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Acknowledgement

Supported by : University of Incheon