L$_p$-C$^*$-Semi-Inner Product Spaces

Abstract

This article introduces the notion of L$_p$-C$^*$-semi-inner product space, a generalization of the concept of C$^*$-semi-inner product space introduced by Gamchi et al., where we consider H\"{o}lder's inequality instead of Cauchy Schwartz' inequality. We establish some basic results L$_p$-C$^*$-semi-inner product spaces, analogous to those valid for C$^*$-semi-inner product spaces and Hilbert C$^*$-modules.

Keywords

• hilbert c$^*$-module
• semi-inner product
• derivation
• anti-derivation