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Seemingly Injective Von Neumann Algebras
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following...
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A characterization of bounded convex approximation properties
The characterization of bounded approximation properties defined by arbitrary operator ideals due to Oja is extended to bounded convex approximation...
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Impact of the Radon–Nikodým property on convex approximation properties
A classical result states that the approximation property (AP) of a dual space X * is metric whenever X * or X ** has the Radon–Nikodým property (RNP)....
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C*-Convex Sets and Completely Positive Maps
We prove a geometric version of an operator valued Hahn–Banach theorem and use it to study sets K that are A -convex over a unital C*-algebra A in the...
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On Norms of Completely Positive Maps
King and Ruskai asked whether the norm of a completely positive map acting between Schatten classes of operators is equal to that of its restriction...
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Normal Fans of Polyhedral Convex Sets
The normal fan of a polyhedral convex set in ℝ n is the collection of its normal cones. The structure of the normal fan reflects the geometry of that...
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Ordered Involutive Operator Spaces
This is a companion to recent papers of the authors; here we construct the ‘noncommutative Shilov boundary’ of a (possibly nonunital) selfadjoint...
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Computing the radius of pointedness of a convex cone
Let Ξ( H ) denote the set of all nonzero closed convex cones in a finite dimensional Hilbert space H . Consider this set equipped with the bounded...
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An Elementary Example of an Order Bound Dual Space that is not Directed
This paper presents an elementary example of an order bounded linear functional on a directed partially ordered vector space that is not equal to the...
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Order and algebra isomorphisms of spaces of regular operators
If E and F are real Banach lattices and there is an algebra and order isomorphism Φ:
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Extreme points of the intersection and the union of some operator balls
The extreme points of the set { A: A * A ≤ R 2 , AA * ≤ R 2 } of operators acting in the n -dimensional Euclidean space are investigated. For n =2 a complete...
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Set of matrices with common Lyapunov solution
We present necessary and sufficient conditions for a set of matrices to coincide with a set of the form { A : HA + A * H > 0} or { T : T ...