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Polar Cones and Cone Capping in Hilbert Spaces

In: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions

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  • Paolo d’Alessandro

Abstract

Polarization is for cones what orthogonal complementation is for linear subspaces. Here we develop in detail the theory of polarization of cones, initiated within lcs, not only recasting in Hilbert space style most of the material developed therein but also adding some further major results, like the decomposition of the space in the direct sum of a closed cone plus its polar cone, which parallels the decomposition in the direct sum of a closed subspace and its orthogonal complement.

Suggested Citation

  • Paolo d’Alessandro, 2025. "Polar Cones and Cone Capping in Hilbert Spaces," Springer Books, in: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions, chapter 0, pages 183-195, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92477-4_11
    DOI: 10.1007/978-3-031-92477-4_11
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