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… 
The Hopf Structure of Some Dual Operator Algebras
We study the Hopf structure of a class of dual operator algebras corresponding to certain semigroups. This class of algebras arises in dilation theory, and includes the noncommutative analytic
On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces
Abstract We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work
Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals
We prove an analogue of the Lebesgue decomposition for continuous functionals on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian operators for which there are quasicentral
Operator algebras for analytic varieties
We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictionsMV of the multiplier algebraM of Drury-Arveson space to a
Ideals in a multiplier algebra on the ball
We study the ideals of the closure of the polynomial multipliers on the Drury-Arveson space. Structural results are obtained by investigating the relation between an ideal and its weak-$*$ closure,
Ueda’s peak set theorem for general von Neumann algebras
We extend Ueda's peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras, to sigma-finite von Neumann algebras (that is, von Neumann algebras with a faithful state; which
Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients
The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the
The Isomorphism Problem for Complete Pick Algebras: A Survey
Complete Pick algebras – these are, roughly, the multiplier algebras in which Pick’s interpolation theorem holds true – have been the focus of much research in the last twenty years or so. All
...
1
2
...

References

SHOWING 1-10 OF 47 REFERENCES
Noncommutative function theory and unique extensions
We generalize to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szeg\"o $L^p$-distance estimate, and classical theorems of F. and M. Riesz, Gleason and
Noncommutative interpolation and Poisson transforms
General results of interpolation (e.g., Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebraF∞ (resp., noncommutative disc algebraAn) with consequences to the interpolation by
A note on absolute continuity in free semigroup algebras
A free semigroup algebra is the weak operator topology closed (nonself-adjoint, unital) algebra generated by n isometries with pairwise orthogonal ranges. The prototype is the algebra generated by
The algebraic structure of non-commutative analytic Toeplitz algebras
The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the
Wandering vectors and the reflexivity of free semigroup algebras
Abstract A free semigroup algebra is the weak-operator-closed (non-self-adjoint) operator algebra generated by n isometries with pairwise orthogonal ranges. A unit vector x is said to be wandering
Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras
The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary
Invariant Subspaces and Hyper‐Reflexivity for Free Semigroup Algebras
A free semigroup algebra is the weak operator topology closed algebra generated by a set of isometries with pairwise orthogonal ranges. The most important example is the left regular free semigroup
The structure of free semigroup algebras
A free semigroup algebra is the wot-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting
The structure of an isometric tuple
An n‐tuple of operators (V1, …, Vn) acting on a Hilbert space H is said to be isometric if the operator [V1⋯Vn]:Hn→H is an isometry. We prove a decomposition for an isometric tuple of operators that
...
1
2
3
4
5
...