$C^{*}$-semi-inner product spaces

Abstract

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 investigated, 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