Open Access
January, 2011 Universal objects in categories of reproducing kernels
Daniel Beltiţă , José E. Galé
Rev. Mat. Iberoamericana 27(1): 123-179 (January, 2011).


We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of $C^*$- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence between reproducing $(-*)$-kernels and the associated Hilbert spaces of sections of vector bundles is made into a functor. We construct reproducing $(-*)$-kernels with universality properties with respect to the operation of pull-back. We show how completely positive maps can be regarded as pull-backs of universal ones linked to the tautological bundle over the Grassmann manifold of the Hilbert space $\ell^2(\mathbb{N})$.


Download Citation

Daniel Beltiţă . José E. Galé . "Universal objects in categories of reproducing kernels." Rev. Mat. Iberoamericana 27 (1) 123 - 179, January, 2011.


Published: January, 2011
First available in Project Euclid: 4 February 2011

zbMATH: 1234.46026
MathSciNet: MR2815734

Primary: 46E22
Secondary: 18A05 , 46L05 , 47B32 , 58B12

Keywords: category theory , completely positive map , Grassmann manifold , reproducing kernel , tautological bundle , universal object , vector bundle

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 1 • January, 2011
Back to Top