Square of ω-hyponormal operators
Copyright policy )Square of ω-hyponormal operators
A bounded linear operator \(T\) on a complex Hilbert space with polar decomposition \(T= U|T|\) is said to be \(w\)-hyponormal if \(||T|^{{1\over 2}} U|T|^{{1\over 2}}|\geq |T|\geq ||T|^{{1\over 2}} U^*|T|^{{1\over 2}}\). It is shown that the square of a \(w\)-hyponormal operator itself is \(w\)-hyponormal. This generalizes a result of Althuge and Wang who for this implication additionally needed the assumption of invertibility for \(T\).
- Kanagawa University Japan
- Niigata University Japan
polar decomposition, Norms (inequalities, more than one norm, etc.) of linear operators, Linear operator inequalities, Subnormal operators, hyponormal operators, etc., \(w\)-hyponormal operator
polar decomposition, Norms (inequalities, more than one norm, etc.) of linear operators, Linear operator inequalities, Subnormal operators, hyponormal operators, etc., \(w\)-hyponormal operator
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