Book chapter
Operators on the Universal Hilbert Space Generated by Transfer Operators
Transfer Operators, Endomorphisms, and Measurable Partitions, pp.93-104
Lecture Notes in Mathematics, Springer International Publishing
06/22/2018
DOI: 10.1007/978-3-319-92417-5_8
Abstract
Starting with a fixed transfer operator (R, σ) on (X,ℬ)\documentclass[12pt]{minimal}
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$$(X, {\mathcal B})$$
\end{document}, we show below that there is then a naturally induced universal Hilbert space ℋ(X)\documentclass[12pt]{minimal}
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$$\mathcal H(X)$$
\end{document} with the property that (R, σ) yields naturally a corresponding isometry in ℋ(X)\documentclass[12pt]{minimal}
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$$\mathcal H(X)$$
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$$\mathcal H(X)$$
\end{document}. With this, we then obtain a rich spectral theory for the transfer operators, for example a setting which may be considered to be an infinite-dimensional Perron-Frobenius theory. Our main results are Theorems 8.12, 8.17, and 8.18.
Details
- Title: Subtitle
- Operators on the Universal Hilbert Space Generated by Transfer Operators
- Creators
- Sergey Bezuglyi - University of IowaPalle E. T Jorgensen - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Transfer Operators, Endomorphisms, and Measurable Partitions, pp.93-104
- Series
- Lecture Notes in Mathematics
- DOI
- 10.1007/978-3-319-92417-5_8
- eISSN
- 1617-9692
- ISSN
- 0075-8434
- Publisher
- Springer International Publishing; Cham
- Language
- English
- Date published
- 06/22/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984240861902771
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