We initiate the study of matrix convexity for operator spaces. define notion compact rectangular convex set, and prove natural analogs Krein-Milman bipolar theorems in this context. deduce a canonical correspondence between sets also introduce boundary representation an space, analog Arveson's conjecture: every space is completely normed by its representations. This yields construction triple e...

A game on a convex geometry is a real-valued function de®ned on the family L of the closed sets of a closure operator which satis®es the ®nite Minkowski±Krein±Milman property. If L is the Boolean algebra 2 N then we obtain a n-person cooperative game. We will introduce convex and quasi-convex games on convex geometries and we will study some properties of the core and the Weber set of these games.

In this paper the problem of locating eigenvalues of negative Krein signature is considered for operators of the form JL, where J is skew-symmetric with bounded inverse and L is self-adjoint. A finite-dimensional matrix, hereafter referred to as the Krein matrix, associated with the eigenvalue problem JLu = λu is constructed with the property that if the Krein matrix has a nontrivial kernel for...

A game on a convex geometry is a real-valued function de0ned on the family L of the closed sets of a closure operator which satis0es the 0nite Minkowski–Krein–Milman property. If L is the boolean algebra 2 then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axiom...

Known properties of ‘‘canonical connections’’ from database theory and of ‘‘closed sets’’ from statistics implicitly define a hypergraph convexity, here called canonical convexity (cconvexity), and provide an efficient algorithm to compute c-convex hulls. We characterize the class of hypergraphs in which c-convexity enjoys the Minkowski–Krein–Milman property. Moreover, we compare c-convexity wi...

We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer optimal control problems, MIOCP). We improve a theorem [25] that states that the solution of a relaxed and convexified problem can be approximated with arbitrary precision by a solution fulfilling the integer requirements. Unlike in previous publications the new ...

Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...

Abstract We formulate a superhedging theorem in the presence of transaction costs and model uncertainty. Asset prices are assumed continuous uncertainty is modeled parametric setting. Our proof relies on new topological framework which no Krein–Smulian type available.

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...