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Hermitian Weighted Composition Operators and Bergman Extremal Functions

Title
Hermitian Weighted Composition Operators and Bergman Extremal Functions
Authors
Cowen C.C.Gunatillake G.Ko E.
Ewha Authors
고응일
SCOPUS Author ID
고응일scopus
Issue Date
2013
Journal Title
Complex Analysis and Operator Theory
ISSN
1661-8254JCR Link
Citation
vol. 7, no. 1, pp. 69 - 99
Indexed
SCIE; SCOPUS WOS scopus
Abstract
Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are (1 - w̄z)-κ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces. © 2011 Springer Basel AG.
DOI
10.1007/s11785-011-0185-7
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자연과학대학 > 수학전공 > Journal papers
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