Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 177-198

SPECTRA OF SOME INVERTIBLE WEIGHTED COMPOSITION OPERATORS ON HARDY AND WEIGHTED BERGMAN SPACES IN THE UNIT BALL

Yong-Xin Gao and Ze-Hua Zhou

Tianjin University, Department of Mathematics
Tianjin 300072, P.R. China; tqlgao 'at' 163.com

Tianjin University, Department of Mathematics, Tianjin 300072, P.R. China
and Tianjin University, Center for Applied Mathematics
Tianjin 300072, P.R. China; zehuazhoumath 'at' aliyun.com, zhzhou 'at' tju.edu.cn

Abstract. In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space H2(BN) and weighted Bergman spaces Aα2(BN), where BN is the unit ball of the N-dimensional complex space. By taking N = 1, BN = D the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on H2(D) or Aα2(D).

2010 Mathematics Subject Classification: Primary 47B38, 32A30; Secondary 32H02, 47B33.

Key words: Weighted composition operator, spectrum, automorphism, Hardy spaces, weighted Bergman spaces, unit ball.

Reference to this article: Y.-X. Gao and Z.-H. Zhou: Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball. Ann. Acad. Sci. Fenn. Math. 41 (2016), 177-198.

Full document as PDF file

doi:10.5186/aasfm.2016.4111

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