Dual cone and polar cone: Difference between revisions

Revision as of 22:19, 22 May 2020

Revision as of 22:19, 22 May 2020

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:<math>C^{\prime} := \left\{ f \in X^{\prime} : \operatorname{Re} \left( f (x) \right) \geq 0 \text{ for all } x \in C \right\}</math>.{{sfn | Schaefer | 1999 | pp=215–222}}

No matter what ''C'' is, ''<math>C^{{sup|\prime}}''</math> will be a convex cone.

If ''C'' ⊆ {0} then <math>C^{\prime} = X^{\prime}</math>.

=== In a Hilbert space (internal dual cone) ===