Hilbert-substructure of Real Measurable Spaces on Reductive Groups, I; Basic TheoryOyadare OO*
Department of Mathematics, Obafemi Awolowo University, Nigeria
- *Corresponding Author:
- Oyadare OO
Department of Mathematics
Obafemi Awolowo University
Ile-Ife, 220005, Nigeria
E-mail: [email protected]
Received date February 13, 2016; Accepted date June 15, 2016; Published date June 20, 2016
Citation: Oyadare OO (2016) Hilbert-substructure of Real Measurable Spaces on Reductive Groups, I; Basic Theory. J Generalized Lie Theory Appl 10:242. doi:10.4172/1736-4337.1000242
Copyright: © 2016 Oyadare OO. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
This paper reconsiders the age-long problem of normed linear spaces which do not admit inner product and shows that, for some subspaces, Fn(G), of real Lp(G)−spaces (when G is a reductive group in the Harish-Chandra class and p=2n), the situation may be rectified, via an outlook which generalizes the fine structure of the Hilbert space, L2(G). This success opens the door for harmonic analysis of unitary representations, G→End(Fn(G)), of G on the Hilbert-substructure Fn(G), which has hitherto been considered impossible.