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(B_N) and weighted Bergman spaces A_α²(B_N), where B_N is the unit ball of the N-dimensional complex space. By taking N = 1, B_N = 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 A_α²(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.

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doi:10.5186/aasfm.2016.4111