Ergodic properties of contraction semigroups in $L_p$, $1
Sato, Ryotaro
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 337-346 / Harvested from Czech Digital Mathematics Library
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Let $\{T(t):t>0\}$ be a strongly continuous semigroup of linear contractions in $L_p$, $10$ a positive linear contraction $P(t)$ in $L_p$ such that $|T(t)f|\leq P(t)|f|$ for all $f\in L_p$, then there exists a strongly continuous semigroup $\{S(t):t>0\}$ of positive linear contractions in $L_p$ such that $|T(t)f|\leq S(t)|f|$ for all $t>0$ and $f\in L_p$. Using this and Akcoglu's dominated ergodic theorem for positive linear contractions in $L_p$, we also prove multiparameter pointwise ergodic and local ergodic theorems for such semigroups.

Publié le : 1994-01-01
Classification:  47A35,  47B38,  47D03,  47D06 
@article{118672,
     author = {Ryotaro Sato},
     title = {Ergodic properties of contraction semigroups in $L\_p$, $1<p<\infty$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {337-346},
     zbl = {0814.47010},
     mrnumber = {1286580},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118672}
}

Sato, Ryotaro. Ergodic properties of contraction semigroups in $L_p$, $1

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