On reproducing property and 2-cocycles

Abstract

In this paper, we study reproducing kernels whose ranges are subsets of a C *algebra or a Hilbert C * -module. In particular, we show how such a reproducing kernel can naturally be expressed in terms of operators on a Hilbert C * -module. We focus on relative reproducing kernels and extend this concept to such spaces associated with cocycles.

On 2-Inner Product Spaces and Reproducing Kernel Property

“…A reproducing kernel Banach space (RKBS in short) on a set X is a reflexive Banach space of functions on X such that its topological dual B † is isometric to a Banach space of functions on X and the point evaluations are continuous linear functionals on both B and B † . More details can be found on [3,4]. Let B be a Banach space.…”