Angular measures and Birkhoff orthogonality in Minkowski planes

On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

Tangent Segments in Minkowski Planes

AMinkowski plane is Euclidean iff the two tangent segments from any exterior point to the unit circle have the same length. MSC 2000: 52A10, 46B20, 46C99, 51M04

Minkowski Planes with Miquelian Pairs

On Reuleaux Triangles in Minkowski Planes

In this paper we prove some results on Reuleaux triangles in (Minkowski or) normed planes. For example, we reprove Wernicke’s result (see [21]) that the unit disc and Reuleaux triangles in a normed plane are homothets if and only if the unit circle is either an affine regular hexagon or a parallelogram. Also we show that the ratio of the area of the unit ball of a Minkowski plane to that of a R...

Orthogonality and Disjointness in Spaces of Measures

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 represented in terms of the notion of measure cone and the mixing distance [1], a specification of the novel concept of direction distance [2]. It turns out tha...