Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300485841> ?p ?o ?g. }
Showing items 1 to 47 of
47
with 100 items per page.
- W4300485841 abstract "Henkin functionals on non-commutative $mathrm{C}^*$-algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our aim in this paper is characterize these functionals through a notion of absolute continuity, inspired by a seminal theorem of Cole and Range. To do this, we recast the problem as a question in non-commutative measure theory. We develop a Glicksberg--Konig--Seever decomposition of the dual space of a $mathrm{C}^*$-algebra into an absolutely continuous part and a singular part, relative to a fixed convex subset of states. Leveraging this tool, we show that Henkin functionals are absolutely continuous with respect to the so-called analytic functionals if and only if a certain compatibility condition is satisfied by the ambient weak-$*$ topology. In contrast with the classical setting, the issue of stability under absolute continuity is not automatic in this non-commutative framework, and we illustrate its key role in sharpening our description of Henkin functionals. Our machinery yields new insight when specialized to the multiplier algebras of the Drury--Arveson space and of the Dirichlet space, and to Popescu's noncommutative disc algebra. As another application, we make a contribution to the theory of non-commutative peak and interpolation sets." @default.
- W4300485841 created "2022-10-03" @default.
- W4300485841 creator A5054796335 @default.
- W4300485841 creator A5076928711 @default.
- W4300485841 date "2021-05-24" @default.
- W4300485841 modified "2023-09-26" @default.
- W4300485841 title "Non-commutative measure theory: Henkin and analytic functionals on $mathrm{C}^*$-algebras" @default.
- W4300485841 doi "https://doi.org/10.48550/arxiv.2105.11295" @default.
- W4300485841 hasPublicationYear "2021" @default.
- W4300485841 type Work @default.
- W4300485841 citedByCount "0" @default.
- W4300485841 crossrefType "posted-content" @default.
- W4300485841 hasAuthorship W4300485841A5054796335 @default.
- W4300485841 hasAuthorship W4300485841A5076928711 @default.
- W4300485841 hasBestOaLocation W43004858411 @default.
- W4300485841 hasConcept C118733216 @default.
- W4300485841 hasConcept C183778304 @default.
- W4300485841 hasConcept C202444582 @default.
- W4300485841 hasConcept C2780009758 @default.
- W4300485841 hasConcept C33923547 @default.
- W4300485841 hasConcept C41008148 @default.
- W4300485841 hasConcept C68797384 @default.
- W4300485841 hasConcept C77088390 @default.
- W4300485841 hasConceptScore W4300485841C118733216 @default.
- W4300485841 hasConceptScore W4300485841C183778304 @default.
- W4300485841 hasConceptScore W4300485841C202444582 @default.
- W4300485841 hasConceptScore W4300485841C2780009758 @default.
- W4300485841 hasConceptScore W4300485841C33923547 @default.
- W4300485841 hasConceptScore W4300485841C41008148 @default.
- W4300485841 hasConceptScore W4300485841C68797384 @default.
- W4300485841 hasConceptScore W4300485841C77088390 @default.
- W4300485841 hasLocation W43004858411 @default.
- W4300485841 hasOpenAccess W4300485841 @default.
- W4300485841 hasPrimaryLocation W43004858411 @default.
- W4300485841 hasRelatedWork W2075936056 @default.
- W4300485841 hasRelatedWork W2124412140 @default.
- W4300485841 hasRelatedWork W2317663302 @default.
- W4300485841 hasRelatedWork W2326718950 @default.
- W4300485841 hasRelatedWork W3128741894 @default.
- W4300485841 hasRelatedWork W3199852337 @default.
- W4300485841 hasRelatedWork W4297231957 @default.
- W4300485841 hasRelatedWork W4297435792 @default.
- W4300485841 hasRelatedWork W792250264 @default.
- W4300485841 hasRelatedWork W954675015 @default.
- W4300485841 isParatext "false" @default.
- W4300485841 isRetracted "false" @default.
- W4300485841 workType "article" @default.