Taiwanese Journal of Mathematics

COUNTEREXAMPLES IN ERGODIC THEORY OF EQUICONTINUOUS SEMIGROUPS OF OPERATORS

J. J. Koliha

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Abstract

The paper gives counterexamples in abstract ergodic theory of an equicontinuous semigroup $\mathcal{S}$ of linear operators on a locally convex space $X$. In particular, it is shown that the orbit of an element $x\in X$ may contain a unique fixed point of $\cal{S}$ without $x$ being necessarily ergodic.

Article information

Source
Taiwanese J. Math., Volume 6, Number 2 (2002), 175-180.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407427

Digital Object Identifier
doi:10.11650/twjm/1500407427

Mathematical Reviews number (MathSciNet)
MR1903134

Zentralblatt MATH identifier
1018.47007

Subjects
Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx] 22A99: None of the above, but in this section

Keywords
equicontinuous semigroup linear operator ergodic element orbit locally convex space Alaoglu--Birkhoff convergence

Citation

Koliha, J. J. COUNTEREXAMPLES IN ERGODIC THEORY OF EQUICONTINUOUS SEMIGROUPS OF OPERATORS. Taiwanese J. Math. 6 (2002), no. 2, 175--180. doi:10.11650/twjm/1500407427. https://projecteuclid.org/euclid.twjm/1500407427


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