Hyponormal Composition Operators
نویسنده
چکیده
In [1] D. Harrington and R. Whitley examined several questions of seminormality for composition operators. In that article they raise the question of finding a measure theoretic characterization of hyponormality for composition operators. In this article we establish criteria for hyponormality for weighted composition operators. By restricting attention to the case of weight function equal to 1 we arrive at a measure theoretic characterization of composition operator hyponormality. Harrington and Whitley also showed that if the measure is finite then hyponormality follows if and only if the transformation is measure preserving; equivalently, if and only if the composition operator is an isometry. We show that there are hyponormal weighted composition operators on finite measure spaces which are not scalar multiples of isometries.
منابع مشابه
On Commutators of Isometries and Hyponormal Operators
A sufficient condition is obtained for two isometries to be unitarily equivalent. Also, a new class of M-hyponormal operator is constructed
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