JournalsrmiVol. 27, No. 1pp. 123–179

Universal objects in categories of reproducing kernels

  • Daniel Beltiţă

    Romanian Academy, Bucharest, Romania
  • José E. Galé

    Universidad de Zaragoza, Spain
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Abstract

We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of CC^*- 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 2(N)\ell^2(\mathbb{N}).

Cite this article

Daniel Beltiţă, José E. Galé, Universal objects in categories of reproducing kernels. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 123–179

DOI 10.4171/RMI/632