A new class of operators and a description of adjoints of composition operators
By C. Cowen, Eva A. Gallardo-Gutiérrez. 2006
59 citations recorded by the source corpus.
Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we com- pute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple val- ued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/99ed6313b0efeb3216241386c42c304293e332dc
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In Applied Mathematics
Citations in the corpus
- Normal and isometric weighted composition operators on the Fock space (2014, methodology): “Weighted composition operators have also been used in descriptions of adjoints of composition operators; see [6] and the references therein.”
- Self-adjoint, unitary, and normal weighted composition operators in several variables (2012, unknown): “5, 6] on commutants of analytic Toeplitz operators on the Hardy space H2 of the unit disk. Weighted composition operators have also been used in descriptions of adjoints of composition operators (see [7] and the references therein). Boundedness and compactness of weighted composition operators on va”