Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball

2013/12/02 by Gao, Yong-Xin, Zhou, Ze-Hua
#32A30 #32H02 #47B33 #47B38 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1312.0471

Abstract

In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space H²(\mathbbB_N) and weighted Bergman spaces A_α²(\mathbbB_N), where \mathbbB_N is the unit ball of the N-dimensional complex space. By taking N=1, \mathbbB_N=\mathbbD the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on H²(\mathbbD) or A_α²(\mathbbD).

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