2012/06/18 by Daniel Beltiţă, Beltita, Daniel, Jośe E. Galé +1
Mathematics · #18A05 (Secondary) #46E22 (Primary) 22E66 #46L05 #47B32 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1206.3969
openalex publication_date 2012/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back operation involving the tautological universal bundle and the classifying morphism of the input kernel. The aforementioned correspondence turns out to be a canonical functor between categories of kernels and linear connections. A number of examples of linear connections including the ones associated to classical kernels, homogeneous reproducing kernels and kernels occurring in the dilation theory for completely positive maps are given, together with their covariant derivatives.