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The class of $\mu$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class…
The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds.…
Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.
In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class $Cvx(K)$ consisting of lower-semi-continuous convex functions defined on a convex set $K$, and its subclass…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
We consider a quantum quasi-relative entropy $S_f^K$ for an operator $K$ and an operator convex function $f$. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the…
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…
We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex…
Consider a Hamiltonian action of a compact Lie group on a compact symplectic manifold. A theorem of Kirwan's says that the image of the momentum mapping intersects the positive Weyl chamber in a convex polytope. I present a new proof of…
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient…
This paper continues the study of Alexandrov-Fenchel inequalities for quermassintegrals for $k$-convex domains. It focuses on the application to the Michael-Simon type inequalities for $k$-curvature operators. The proof uses optimal…
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…
Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…
We present several applications of matrix-theoretic inequalities to the magnitude of metric spaces. We first resolve an open problem by showing that the magnitude of any finite metric space of negative type is less than or equal to its…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…
We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any…