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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-11212-6_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11211-9
Online ISBN: 978-3-642-11212-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
