Lyapunov's theorem for continuous frames

Akemann and Weaver (2014) have shown a remarkable extension of Weaver's KS_r Conjecture (2004) in the form of approximate Lyapunov's theorem. This was made possible thanks to the breakthrough solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava (2015). In this paper w...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-09, Vol.146 (9), p.3825-3838
Main Author: BOWNIK, MARCIN
Format: Article
Language:English
Subjects:
B. ANALYSIS
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Summary:Akemann and Weaver (2014) have shown a remarkable extension of Weaver's KS_r Conjecture (2004) in the form of approximate Lyapunov's theorem. This was made possible thanks to the breakthrough solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava (2015). In this paper we show a similar type of Lyapunov's theorem for continuous frames on non-atomic measure spaces. In contrast with discrete frames, the proof of this result does not rely on the recent solution of the Kadison-Singer problem.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14088