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SPECTRA OF LINEAR FRACTIONAL COMPOSITION OPERATORS ON THE GROWTH SPACE AND BLOCH SPACE OF THE UPPER HALF-PLANE

  • SHI-AN HAN (a1) and ZE-HUA ZHOU (a2)
Abstract

In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.

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The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11771323; 11371276).

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