Mean ergodicity and spectrum of the Cesàro operator on weighted $$c_0$$ c 0 spaces

Mean ergodicity and spectrum of the Cesàro operator on weighted $$c_0$$ c 0 spaces A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator $$\mathsf {C}$$ C acting on the weighted Banach sequence space $$c_0(w)$$ c 0 ( w ) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of $$c_0$$ c 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Mean ergodicity and spectrum of the Cesàro operator on weighted $$c_0$$ c 0 spaces

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Publisher
Springer International Publishing
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0385-x
Publisher site
See Article on Publisher Site

Abstract

A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator $$\mathsf {C}$$ C acting on the weighted Banach sequence space $$c_0(w)$$ c 0 ( w ) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of $$c_0$$ c 0 .

Journal

PositivitySpringer Journals

Published: Nov 30, 2015

References

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