A note on the equation \(Y=(I-T)X\) in \(L^1\) (Q1305186)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on the equation \(Y=(I-T)X\) in \(L^1\) |
scientific article; zbMATH DE number 1345977
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the equation \(Y=(I-T)X\) in \(L^1\) |
scientific article; zbMATH DE number 1345977 |
Statements
A note on the equation \(Y=(I-T)X\) in \(L^1\) (English)
0 references
18 May 2000
0 references
Let \(T\) be a power bounded operator on \(L^1\) such that for all sequences \((h_n)\) with \(h_n\to 0\) a.e., also \(Th_n\to 0\) a.e. For \(f\in L^1\) the following conditions are equivalent: \hskip 17mm (1) \(\sup_n\|\sum^n_{k=1} T^kf\|_1< \infty\) \hskip 17mm and \hskip 17mm (2) there exists \(g\in L^1\) with \(f= g-Tg\).
0 references
mean ergodic theorem
0 references
power bounded operator
0 references
