Bicommutants of multiplication operators

Bicommutants of multiplication operators We consider the well-known problem: when does an analogue of von Neumann Double Commutant Theorem hold for a multiplication operator on a Banach space of functions? We get an affirmative answer to the above problem for multiplication operators on C(K), where K is a locally connected continuum. In the second part of the paper we solve the above mentioned problem for multiplication operators on C (1)[0, 1] in the case when the multiplier is either a polynomial or a non-decreasing function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Bicommutants of multiplication operators

Positivity , Volume 14 (4) – Jul 13, 2010

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0062-z
Publisher site
See Article on Publisher Site

Abstract

We consider the well-known problem: when does an analogue of von Neumann Double Commutant Theorem hold for a multiplication operator on a Banach space of functions? We get an affirmative answer to the above problem for multiplication operators on C(K), where K is a locally connected continuum. In the second part of the paper we solve the above mentioned problem for multiplication operators on C (1)[0, 1] in the case when the multiplier is either a polynomial or a non-decreasing function.

Journal

PositivitySpringer Journals

Published: Jul 13, 2010

References

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