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Vector Measures, Integration and Related Topics pp 215–229Cite as

Logarithms of Invertible Isometries, Spectral Decompositions and Ergodic Multipliers

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 201))

Abstract

Firstly, we consider when certain invertible isometries on Banach spaces have (bounded linear) logarithms and when they are trigonometrically well bounded, i.e., have spectral decompositions similar to that of a unitary operator. We then survey aspects of the theory of trigonometrically well-bounded operators, including an outline of some recent results.

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Author information

Authors and Affiliations

  1. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh James Clerk Maxwell Building, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

    T. Alastair Gillespie

Authors
  1. T. Alastair Gillespie
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Editor information

Editors and Affiliations

  1. Facultad de Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain

    Guillermo P. Curbera

  2. Fachbereich 6: Mathematik, Universität Siegen, 57068, Siegen, Germany

    Gerd Mockenhaupt

  3. Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85072, Eichstätt, Germany

    Werner J. Ricker

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Gillespie, T.A. (2009). Logarithms of Invertible Isometries, Spectral Decompositions and Ergodic Multipliers. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_20

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