Posinormal terraced matrices
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This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ℓ^2; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that MM^*=M^*PM for some positive operator P on ℓ^2; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint M^* to be posinormal, and it is observed that, unless M is essentially trivial, M^* cannot be hyponormal. A few examples are considered that exhibit special behavior.
Abstract
This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ℓ^2; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that MM^*=M^*PM for some positive operator P on ℓ^2; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint M^* to be posinormal, and it is observed that, unless M is essentially trivial, M^* cannot be hyponormal. A few examples are considered that exhibit special behavior.
참고문헌 (10)
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