On order bounded weighted composition operators between Dirichlet spaces

On order bounded weighted composition operators between Dirichlet spaces Recently, Gao et al. (Chin Ann Math 37B:585–594, 2016) proved a sufficient condition for order boundedness of a weighted composition operator acting between Dirichlet spaces. In this paper, we prove that their condition is a necessary and sufficient condition for order boundedness of a weighted composition operator acting between these spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On order bounded weighted composition operators between Dirichlet spaces

Positivity , Volume 21 (3) – Dec 19, 2016

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing
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/s11117-016-0462-9
Publisher site
See Article on Publisher Site

Abstract

Recently, Gao et al. (Chin Ann Math 37B:585–594, 2016) proved a sufficient condition for order boundedness of a weighted composition operator acting between Dirichlet spaces. In this paper, we prove that their condition is a necessary and sufficient condition for order boundedness of a weighted composition operator acting between these spaces.

Journal

PositivitySpringer Journals

Published: Dec 19, 2016

References

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