Hermitian Weighted Composition Operators and Bergman Extremal Functions
- 주제(키워드) Bergman inner function , Composition operator , Hermitian operator , Normal operator , Projected kernel function , Spectral measure , Weighted Bergman space , Weighted composition operator , Weighted Hardy space
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Birkhaeuser
- 발행년도 2013
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000094606
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s11785-011-0185-7
초록/요약
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.
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