C-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert C -modules which are pre-Finsler modules, namely, C -semi-inner product spaces. Some properties and results of such spaces are in vestigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on C -semi-inner product spaces.

Keywords:

Semi-inner product space , Hilbert C -module , C-algebra