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Isometries and Hermitian Operators on Zygmund Spaces

  Published:2015-02-17
 Printed: Jun 2015
  • Fernanda Botelho,
    Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA
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Abstract

In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords: Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries
MSC Classifications: 46E15, 47B15, 47B38 show english descriptions Banach spaces of continuous, differentiable or analytic functions
Hermitian and normal operators (spectral measures, functional calculus, etc.)
Operators on function spaces (general)
46E15 - Banach spaces of continuous, differentiable or analytic functions
47B15 - Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B38 - Operators on function spaces (general)
 

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