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Spectral Theory of Unitary Operators

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1294)

Abstract

We wish to classify isometric operators on Hilbert spaces, up to unitary equivalence (or spectral equivalence). We introduce for this purpose different notions of the spectral theory of unitary operators, such as : spectral measure, maximal spectral type, spectral multiplicity, multiplicity function, etc.; we establish two versions of the spectral decomposition theorem for these operators, with our familiar notations. The definitions and results will be used in the next chapter where we focus on dynamical systems, and later, when we study the spectral properties of substitutive sequences.

Keywords

  • Unitary Operator
  • Spectral Measure
  • Spectral Theory
  • Trigonometric Polynomial
  • Separable Hilbert Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Martine Queffélec .

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© 2010 Springer-Verlag Berlin Heidelberg

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Queffélec, M. (2010). Spectral Theory of Unitary Operators. In: Substitution Dynamical Systems - Spectral Analysis. Lecture Notes in Mathematics(), vol 1294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11212-6_2

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