关于紧算子的infinite dimensional随机积的谱
On the spectrum of infinite dimensional random products of compact operators
摘要：
考虑了一个无穷维可分希尔伯特空间及其紧可积上圈族，其中f是一个动力系统。假设f作用在紧致T2空间X上，且在非空开集上保持正的Borel正则遍历测度，我们得到结论：存在余圈的剩余子集，在该余圈的剩余子集中，几乎对每个x，沿着x的轨道的Oseledets-Ruelle分解都是支配的，或者具有平凡谱.
英文摘要：
We consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic measure which is positive on non-empty open sets, we conclude that there is a residual subset of cocycles within which, for almost every x, either the Oseledets-Ruelle's decomposition along the orbit of x is dominated or has a trivial spectrum.
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