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Multiplicative Isometries and Isometric Zero-Divisors

Published online by Cambridge University Press:  20 November 2018

Alexandru Aleman ,
Peter Duren ,
María J. Martín  and
Dragan Vukotić
Alexandru Aleman*
Affiliation:
Department of Mathematics, Lund University, P. O. Box 118, S-221 00 Lund, Sweden
Peter Duren*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1043, USA
María J. Martín*
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Dragan Vukotić*
Affiliation:
Departamento de Matemáticas & ICMAT CSIC-UAM-UC3M-UCM, Universidad Autónoma de Madrid, 28049 Madrid, Spain
*
[email protected]
[email protected]
[email protected]
[email protected]
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Abstract

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For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

Keywords

30H0546E15Banach spaces of analytic functionsHardy spacesBergman spacesBloch spaceDirichlet spaceDirichlet-type spacespointwise multiplierscoefficient multipliersisometriesisometric zerodivisors
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 5 , 01 October 2010 , pp. 961 - 974
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

The research of the second, third, and fourth authors is supported by MICINN grant MTM2009-14694-C02-01, Spain. The third and fourth authors are partially supported by the Thematic Network MTM2008-02829-E fromMICINN. The fourth author is also partially supported by the European Science Foundation Network HCAA (“Harmonic and Complex Analysis and Applications”).

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