# A non-self-adjoint Lebesgue decomposition

@article{Kennedy2013ANL, title={A non-self-adjoint Lebesgue decomposition}, author={Matthew Kennedy and Dilian Yang}, journal={arXiv: Operator Algebras}, year={2013} }

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…

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