Power bounded operators and the mean ergodic theorem for subsequences

On the Mean Ergodic Theorem for Subsequences

With these assumptions we have T defined for every integer n as a 1-1, onto, bimeasurable transformation. Henceforth we shall assume that every set considered is measurable, i.e. an element of a. We shall say that P is invariant if P(A) =P(TA) for every set A, P is ergodic if P is invariant and if P(U^L_oo TA) = 1 for every set A for which P(A) > 0 , and finally P is strongly mixing if P is inv...

An L Ergodic Theorem for Sparse Random Subsequences

We prove an L subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally L-good sequences nearly as sparse as the set of squares. In the process, we prove that a certain deterministic condition implies a weak maximal inequality for a sequence of l convolution operators (Prop. 3.1).

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

Spectral Theorem for Bounded Self-adjoint Operators

Diagonalization is one of the most important topics one learns in an elementary linear algebra course. Unfortunately, it only works on finite dimensional vector spaces, where linear operators can be represented by finite matrices. Later, one encounters infinite dimensional vector spaces (spaces of sequences, for example), where linear operators can be thought of as ”infinite matrices”. Extendin...

Power - Bounded Operators and Relatednorm