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Title: A note on self-dual cones in Hilbert spaces
Authors: Jayaraman, Sachindranath
Keywords: Self-dual / regular cone;Nonnegative reflexive generalized inverse;Riesz basis;Cono auto dual / regular;Inversores reflexivos no negativos generalizados;Base Riesz
Issue Date: 2013
Publisher: Universidad de Extremadura
Abstract: A result of Tam says that if a nonnegative matrix A has a nonnegative generalized inverse X (that is, X satisfies the equation AXA = A) then, A(R₊ⁿ) = R(A) ∩ R₊ᵐ and are simplicial (the image of the nonnegative orthant under an invertible linear map). Although in general, a simplicial cone need not be self-dual, there is another inner product with respect to which it is self-dual. The aim of this note to bring out an analoge of this in infinite dimensional separable Hilbert spaces, although there is no notion of simpliciality in such spaces.
Appears in Collections:Extracta Mathematicae Vol. 28, nº 2 (2013)

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