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Multiplicative Isometries and Isometric Zero-Divisors
  Published:2010-06-18
 Printed: Oct 2010
Canadian Journal of Mathematics
  • Alexandru Aleman,
    Department of Mathematics, Lund University, P.O. Box 118, S-221 00 Lund, Sweden
  • Peter Duren,
    Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043, USA
  • María J. Martín,
    Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
  • Dragan Vukotić,
    Departamento de Matemáticas & ICMAT CSIC-UAM-UC3M-UCM, Universidad Autónoma de Madrid, 28049 Madrid, Spain
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Abstract

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: Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisors Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisors
MSC Classifications: 30H05, 46E15 show english descriptions Bounded analytic functions
Banach spaces of continuous, differentiable or analytic functions 30H05 - Bounded analytic functions
46E15 - Banach spaces of continuous, differentiable or analytic functions
 
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