Related papers: Subadditive retractions on cones and asymmetric ve…
We consider the problem of isotonic regression, where the underlying signal $x$ is assumed to satisfy a monotonicity constraint, that is, $x$ lies in the cone $\{ x\in\mathbb{R}^n : x_1 \leq \dots \leq x_n\}$. We study the isotonic…
The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.
Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that collectively order to norm bounded sets are bounded in the operator norm…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain…
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a…
Well-known subadditivity results for positive operators (of Brown-Kosaki and Rotfeld/Ando-Zhan types) are extended to Hermitian and normal ones. Applications to Cartesian decomposition and block-matrices are given.
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisation of when one Beta distribution is smaller than another…
The trace anomaly and anomaly-induced action are evaluated for the two-dimensional $2D$ vector theory with classical conformal symmetry. Implementing local conformal symmetry while preserving the gauge invariance requires either giving up…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
As the reversed version of usual symmetric norms, we introduce the notion of symmetric anti-norms $\|\cdot\|_!$ defined on the positive operators affiliated with a finite von Neumann algebra with a finite normal trace. Related to symmetric…
We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…
Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This…
Here we look at some geometric properties related to connectedness and topological dimension 0, especially in connection with norms on vector spaces over fields with absolute value functions, which may be non-archimedian.