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Research Article Open Access
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.
Reductive groups, Hilbert spaces, Orthogonal polynomials, Algebra, Combinatorics, Deformations Theory, Geometry, Harmonic Analysis, Homological Algebra, Homotopical Algebra, Latin Squares, Lie Theory, Lie Triple Systems, Loop Algebra, Operad Theory, Quantum Group, Quasi-Group, Representation theory, Super Algebras, Lie Superalgebra, Symmetric Spaces, Topologies, Lie Algebra