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Entropies of commuting transformations on Hilbert spaces

  • * Corresponding author: Zhiming Li

    * Corresponding author: Zhiming Li 

The first author is supported by NSFC (No: 11871394) and Natural Science Foundation of Shaanxi Province (2020JC-39), the second author is supported by NSFC (No: 11771118)

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  • By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesin's entropy formula and SRB measures of a finitely generated random transformations on such space via its commuting generators. Moreover, as an application, we give a formula of Friedland's entropy for certain $ C^{2} $ $ \mathbb{N}^2 $-actions.

    Mathematics Subject Classification: Primary:37H15, 37A35, 37C85;Secondary:37H99, 37D20.


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