Taiwanese Journal of Mathematics


Hong-Kun Xu and Isao Yamada

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Let $T$ be a linear power bounded operator on a Banach space $X$ and let $S_{\lambda} = (1−\lambda)I + \lambda T$ be the averaged map of $T$, where $\lambda \in (0,1)$. It is shown that $S_{\lambda}$ is asymptotically regular on $X$; that is, $\lim_{n \to \infty} \| S_{\lambda}^{n}x - S_{\lambda}^{n+1}x \| = 0$ for every $x \in X$. Hence the sequence $\{S_{\lambda}^{n}x\}$ converges strongly provided it has a weak cluster point.

Article information

Taiwanese J. Math., Volume 10, Number 2 (2006), 417-429.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 47B44: Accretive operators, dissipative operators, etc.
Secondary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

mean ergodic theorem linear power bounded operator asymptotic regularity averaged mapping


Xu, Hong-Kun; Yamada, Isao. ASYMPTOTIC REGULARITY OF LINEAR POWER BOUNDED OPERATORS. Taiwanese J. Math. 10 (2006), no. 2, 417--429. doi:10.11650/twjm/1500403834. https://projecteuclid.org/euclid.twjm/1500403834

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