|
|||||
 |
|
|
|
|
|
A
non-self-adjoint Lebesgue decomposition
Matthew Kennedy and Dilian Yang |
|
Vol. 7 (2014), No. 2, 497–512
|
Abstract |
|
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. |
Keywords
Lebesgue decomposition, extended F. and M. Riesz theorem,
unique predual, Drury–Arveson space
|
Mathematical Subject Classification 2010
Primary: 46B04, 47B32, 47L50, 47L55
|
Milestones
Received: 4 July 2013
Revised: 27 October 2013
Accepted: 27 November 2013
Published: 30 May 2014
|
Authors |
| Matthew Kennedy | |
| School of Mathematics and
Statistics Carleton University 1125 Colonel By Drive Ottawa, ON K1S 5B6 Canada |
|
| Dilian Yang | |
| Department of Mathematics and
Statistics University of Windsor 401 Sunset Avenue Windsor, ON N9B 3P4 Canada |
|
|
