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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. |
| URI: | http://hdl.handle.net/10662/10277 |
| Appears in Collections: | Extracta Mathematicae Vol. 28, nº 2 (2013) |
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|---|---|---|---|---|
| 2605-5686_28_2_225.pdf | 93,47 kB | Adobe PDF | View/Open |
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