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In this chapter we discuss three fundamental decompositions for linear contractions on Hilbert spaces, which turn out to be important for ergodic theorems, namely the von Neumann decomposition, the rational spectrum decomposition, and the Jacobsde LeeuwGlicksberg decomposition. On our way we encounter the Szökefalvi-Nagy-Foias and Wold decompositions as well as unitary dilations. We also revisit weak mixing.

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Decompositions in Hilbert Spaces

  • 章节

  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

In this chapter we discuss three fundamental decompositions for linear contractions on Hilbert spaces, which turn out to be important for ergodic theorems, namely the von Neumann decomposition, the rational spectrum decomposition, and the Jacobsde LeeuwGlicksberg decomposition. On our way we encounter the Szökefalvi-Nagy-Foias and Wold decompositions as well as unitary dilations. We also revisit weak mixing.