Taiwanese Journal of Mathematics

ON ERGODIC AVERAGES AND THE RANGE OF A CLOSED OPERATOR

Ryotaro Sato

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Abstract

For a $\gamma$-th order Cesàro mean bounded linear operator $T$ on a Banach space $X$, we characterize the range $R(A)$ of the operator $A = T-I$, by using an $A$-ergodic net and its companion net which were introduced by Dotson and developed by Shaw. Similarly, if $A$ is the generator of a $\gamma$-th order Cesàro mean bounded $C_{0}$-semigroup (or strongly continuous cosine operator function) of bounded linear operators on $X$, then we characterize the range $R(A)$.

Article information

Source
Taiwanese J. Math., Volume 10, Number 5 (2006), 1193-1223.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500557298

Digital Object Identifier
doi:10.11650/twjm/1500557298

Mathematical Reviews number (MathSciNet)
MR2253374

Zentralblatt MATH identifier
1124.47008

Subjects
Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx] 47A50: Equations and inequalities involving linear operators, with vector unknowns 47D05 47D09: Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]

Keywords
Banach space $\gamma$-th Order Cesàro mean bounded operator closed operator range and domain generator resolvent $C_{0}$-semigroup cosine operator function ergodic net and its companion net mean ergodic theorem cohomology equation cobounda

Citation

Sato, Ryotaro. ON ERGODIC AVERAGES AND THE RANGE OF A CLOSED OPERATOR. Taiwanese J. Math. 10 (2006), no. 5, 1193--1223. doi:10.11650/twjm/1500557298. https://projecteuclid.org/euclid.twjm/1500557298


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