Bipolar theorem

Known as: Bipolar

In mathematics, the bipolar theorem is a theorem in convex analysis which provides necessary and sufficient conditions for a cone to be equal to its…

Papers overview

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2017

We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact…

2016

The spaces ${\mathcal S}'/{\mathcal P}$ equipped with the quotient topology and ${\mathcal S}'_\infty$ equipped with the weak…

2012

In this note duality properties of quantum cones are investigated. We propose a bipolar theorem for quantum cones, which provides…

2007

We extend the Bipolar Theorem of Kramkov and Schachermayer(12) to the space of nonnegative càdlàg supermartingales on a filtered…

2005

Motivated by applications in financial mathematics, Ref. 3 showed that, although $$L^{0}(\mathbb{R}_{+}; \Omega, {\cal F…

2003

Motivated by applications in financial mathematics, [3] showed that, although L(R+; Ω,F ,P) fails to be locally convex, an…

1999

A consequence of the Hahn-Banach theorem is the classical bipolar theorem which states that the bipolar of a subset of a locally…

1999

1989

We prove that the classic interpolation spaces of Calderón can be defined using spaces of functions that satisfy weaket…

1988

We study the spaces E which are isometric to their biduals E**, and satisfy dim(E** /E) ,O o,i 0, 1 0] are isomorphic to their…