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.

中文翻译：

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Hilbert空间上的换向变换的熵

通过在可分离的无限维希尔伯特空间上建立换向变换的乘性遍历定理，本文研究了通过换向生成器在这种空间上有限生成的随机变换的Pesin熵公式和SRB测度。此外，作为应用，我们给出了某些$ C ^ {2} $ $ \ mathbb {N} ^ 2 $-动作的Friedland熵公式。