Generalized Riesz Representation Theorem in n-Hilbert Space

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, we develop a generalized version of Riesz representation theorem with respect to b-sesquilinear functional in
n-Hilbert space.

Key words and phrases. Riesz representation theorem, sesquilinear functional, polarization identity, linear n-normed space, n-inner product space.

2010 Mathematics Subject Classification. 41A65, 41A15, 46B07, 46B25.