2007/07/05 by Daniel Beltiţă, Daniel Beltita, Beltita, Daniel +3
Mathematics · #22E65 #43A85 #46E22 #46L05 #46L07 #46L55 #47B38 #58B12 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.DG #math.OA #msc:22E65 #msc:43A85 #msc:46E22 #msc:46L05 #msc:46L07 #msc:46L55 #msc:47B38 #msc:58B12
paper · pdf · doi:10.48550/arxiv.0707.0806
45 pages
openalex publication_date 2007/07/05 · arxiv created 2008/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Representations of C^*-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with involutive diffeomorphisms defined on the base spaces of the bundles. Applications of this technique to dilation theory of completely positive maps are explored and the critical role of complexified homogeneous spaces in connection with the Stinespring dilations is pointed out. The general results are further illustrated by a discussion of several specific topics, including similarity orbits of representations of amenable Banach algebras, similarity orbits of conditional expectations, geometric models of representations of Cuntz algebras, the relationship to endomorphisms of \mathcal B(\mathcal H), and non-commutative stochastic analysis.