Separation theorems for bounded convex sets of bounded operators

Published 27 May 2024 in math.OA | (2405.17614v1)

Abstract: We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary $C^*$-algebra (respectively, von Neumann algebra), and provide applications of these results to the majorization theory.

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Equality of ultraweak and operator-norm closures of convex hulls of unitary orbits

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