Generalized Riesz Representation Theorem in n-Hilbert space

TL;DR

This paper extends the Riesz representation theorem to n-Hilbert spaces by defining b-sesquilinear functionals, establishing polarization identities, and proving a generalized Schwarz inequality.

Contribution

It introduces a generalized Riesz representation theorem for b-sesquilinear functionals in n-Hilbert spaces, expanding the theoretical framework.

Findings

Established polarization identities in n-Hilbert spaces

Proved a generalized Schwarz inequality

Developed a generalized Riesz representation theorem

Abstract

In respect of b-linear functional, Riesz representation theorem in n-Hilbert space have been proved. We define b-sesquilinear functional in n-Hilbert space and establish the polarization identities. A generalized form of the Schwarz inequality in n-Hilbert space is being discussed. Finally, a generalized version of Riesz representation theorem with respect to b-sesquilinear functional in n-Hilbert space have been developed.