Reproducing kernel Hilbert C*-modules and kernels associated with cocycles

Abstract

In this paper we discuss reproducing kernels whose ranges are contained in a C*-algebra or a Hilbert C*-module. Using the construction of a reproducing Hilbert C*-module associated with a reproducing kernel, we show how such a reproducing kernel can naturally be expressed in terms of operators on a Hilbert C*-module using representations on Hilbert C*-modules. We prove that for each positive definite G-kernel associated with a cocycle there is a representation associated with an operator-valued cocycle on the corresponding Hilbert C*-module. Finally, some examples will be considered.