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Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

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Chen Y., Lee Y., Yu T.

Studia Mathematica

2014

tom 220

nr 2

141-156

We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if ϕ = λz² for some unimodular constant λ.

Ograniczanie wyników

1 Studia Mathematica

1 Chen Y.

1 Lee Y.

1 Yu T.

1 2014

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Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space