Isometries and spectra of multiplication operators on the Bloch space

Details Isometries and spectra of multiplication operators on the Bloch space Isometries and spectra of multiplication operators on the Bloch space

2008-09-19

arxiv.org/abs/0809.3278v2

Mathematics

Functional Analysis

accepted to the Bulletin of the Australian Mathematical Society

Scientific paper

In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

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