# Lebesgue decomposition of non-commutative measures.

@inproceedings{Jury2019LebesgueDO, title={Lebesgue decomposition of non-commutative measures.}, author={Michael T. Jury and Robert T.W. Martin}, year={2019} }

The Riesz-Markov theorem identifies any positive, finite, and regular Borel measure on the complex unit circle with a positive linear functional on the continuous functions. By the Weierstrass approximation theorem, the continuous functions are obtained as the norm closure of the Disk Algebra and its conjugates. Here, the Disk Algebra can be viewed as the unital norm-closed operator algebra of the shift operator on the Hardy Space, $H^2$ of the disk.
Replacing square-summable Taylor series… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

## Fatou's Theorem for Non-commutative Measures

VIEW 3 EXCERPTS

CITES RESULTS & BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 34 REFERENCES

## Absolutely continuous representations and a Kaplansky density theorem for free semigroup algebras

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Absolute continuity for operator valued completely positive maps on C-algebras

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## On subalgebras of $C^*$-algebras

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Fatou's Theorem for Non-commutative Measures

VIEW 3 EXCERPTS

## A note on absolute continuity in free semigroup algebras

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Column extreme multipliers of the Free Hardy space

VIEW 3 EXCERPTS

## The Smirnov classes for Drury-Arveson and Fock space

VIEW 1 EXCERPT