A volume-based approach to the multiplicative ergodic theorem on Banach spaces

A Concise Proof of the Multiplicative Ergodic Theorem on Banach Spaces

We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner [1] and T. Tao [11].

Oseledec’s Multiplicative Ergodic Theorem

These are notes for a talk in the Junior Geometry seminar at UT Austin on Oseledec’s multiplicative ergodic theorem given in Fall 2002. The purpose of the notes is to insure that I know, or at least am convinced that I think I know, what I am talking about. They contain far more material than the talks themselves, constituting a complete proof of the discrete-time version of the multiplicative ...

A multiplicative Banach-Stone theorem

The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...