English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We construct a non-commutative Aleksandrov-Clark measure for any element inthe operator-valued free Schur class, the closed unit ball of the free Toeplitzalgebra of vector-valued full Fock space over $\mathbb{C} ^d$. Here, the free(analytic) Toeplitz algebra is the unital weak operator topology (WOT)-closedalgebra generated by the component operators of the free shift, the rowisometry of left creation operators. This defines a bijection between the freeoperator-valued Schur class and completely positive maps (non-commutative ACmeasures) on the operator system of the free disk algebra, the norm-closedalgebra generated by the free shift. Identifying Drury-Arveson space withsymmetric Fock space, we determine the relationship between the non-commutativeAC measures for elements of the operator-valued commutative Schur class (theclosed unit ball of the WOT-closed Toeplitz algebra generated by the Arvesonshift) and the AC measures of their free liftings to the free Schur class.

Non-commutative Clark measures for the free and abelian Toeplitz algebras