On the Spectrum of Infinite Dimensional Random Products of Compact Operators
نویسنده
چکیده
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 OseledetsRuelle’s decomposition along the orbit of x is dominated or has a trivial spectrum. MSC 2000: primary 37H15, 37D08; secondary 47B80. keywords: Random operators; dominated splitting; multiplicative ergodic theorem; Lyapunov exponents.
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