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Title: A NON-COMMUTATIVE F. & M. RIESZ THEOREM
We extend results on complex analytic measures on the complex unit circle to a non-commutative multivariate setting. Identifying continuous linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz C ∗ - algebra, the free disk operator system, with non-commutative (NC) analogues of complex measures, we refine a previously developed Lebesgue decompo- sition for positive NC measures to establish an NC version of the Frigyes and Marcel Riesz Theorem for “analytic” measures, i.e. complex measures with vanishing positive moments. The proof relies on novel results on the order properties of positive NC measures that we develop and extend from classical measure theory.  more » « less
Award ID(s):
1900364
PAR ID:
10470434
Author(s) / Creator(s):
; ;
Publisher / Repository:
Theta Foundation
Date Published:
Journal Name:
Journal of Operator Theory
Volume:
90
Issue:
2
ISSN:
0379-4024
Subject(s) / Keyword(s):
Non-commutative disc algebra, F. and M. Riesz Theorem, operator sys- tems, Cuntz and Cuntz–Toeplitz algebras, non-commutative measure theory.
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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