Fundamental Properties of Composition Operatorsin Other (Other) by Dgoodz19
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154 4 Hankel Operators
T Hei Hei T Hei Hdei . 2 , it follows that Hdei 0, and thus that
Since dei is in ei H
T Hei Hei T 0.
Also, since c, we have Hei Hcei ei , and therefore
T Hei Hcei T Hei T 0. 2 , Hcei 0. Therefore
Since cei is in ei H
T Hei Hei T .
It follows that if H is a multiple of Hei , then H commutes with T . To prove the converse, suppose that HT T H. Multiplying T H on the right by U , using the fact...