LYAPUNOV'S THEOREM FOR CONTINUOUS FRAMES.

Akemann and Weaver (2014) have shown a remarkable extension of Weaver's KSr 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. [ABSTRACT FROM AUTHOR]