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2014 A non-self-adjoint Lebesgue decomposition
Matthew Kennedy, Dilian Yang
Anal. PDE 7(2): 497-512 (2014). DOI: 10.2140/apde.2014.7.497


We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna–Pick space, and in particular the multiplier algebra of the Drury–Arveson space. Our main result is a Lebesgue decomposition expressing every linear functional as the sum of an absolutely continuous (i.e., weak-* continuous) linear functional and a singular linear functional that is far from being absolutely continuous. This is a non-self-adjoint analogue of Takesaki’s decomposition theorem for linear functionals on von Neumann algebras. We apply our decomposition theorem to prove that the predual of every algebra in this class is (strongly) unique.


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Matthew Kennedy. Dilian Yang. "A non-self-adjoint Lebesgue decomposition." Anal. PDE 7 (2) 497 - 512, 2014.


Received: 4 July 2013; Revised: 27 October 2013; Accepted: 27 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1302.47104
MathSciNet: MR3218817
Digital Object Identifier: 10.2140/apde.2014.7.497

Primary: 46B04 , 47B32 , 47L50 , 47L55

Keywords: Drury–Arveson space , extended F. and M. Riesz theorem , Lebesgue decomposition , unique predual

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.7 • No. 2 • 2014
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