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July, 2011 Invariant means on bounded vector-valued functions
Yuan-Chuan LI
J. Math. Soc. Japan 63(3): 819-836 (July, 2011). DOI: 10.2969/jmsj/06330819

Abstract

Shioji and Takahashi proved that for every bounded sequence $\{a_n\}^{\infty}_{n=0}$ of real numbers, $$\{\phi(\{a_n\}^{\infty}_{n=0}) \: | \: \phi \mathrm{\: is \: a \: Banach \: limit} \}$$ $$\: \: = \displaystyle\bigcap\limits_{j=1}^{\infty} \overline{\mathrm{co}} \{(n+1)^-1 \displaystyle\sum\limits_{k=0}^n a_{k+m} \: | \: n \geq j, m \geq 0 \}.$$ We generalize this result to bounded sequences of vectors and also apply it to bounded measurable functions.

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Yuan-Chuan LI. "Invariant means on bounded vector-valued functions." J. Math. Soc. Japan 63 (3) 819 - 836, July, 2011. https://doi.org/10.2969/jmsj/06330819

Information

Published: July, 2011
First available in Project Euclid: 1 August 2011

zbMATH: 1232.40006
MathSciNet: MR2836746
Digital Object Identifier: 10.2969/jmsj/06330819

Subjects:
Primary: 40G05 , 47A35
Secondary: 40E05

Keywords: Abel limit , Banach limit , Cesáro limit , ergodic net , ‎mean‎ , semi-ergodic net , strongly almost convergent , weakly almost convergent , σ-limit

Rights: Copyright © 2011 Mathematical Society of Japan

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Vol.63 • No. 3 • July, 2011
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