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ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 February 2009

ROBERT F. ALLEN  and
FLAVIA COLONNA
ROBERT F. ALLEN
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA (email: rallen2@gmu.edu)
FLAVIA COLONNA*
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA (email: fcolonna@gmu.edu)
*
✉For correspondence; e-mail: fcolonna@gmu.edu
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Abstract

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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.

Keywords

multiplication operatorsBloch spacelittle Bloch space

MSC classification

Secondary: 47B38: Operators on function spaces (general)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 147 - 160
Copyright
Copyright © Australian Mathematical Society 2009

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