Related papers: Bands in partially ordered vector spaces with orde…
Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we…
Disjointness, bands, and band projections are a classical and essential part of the structure theory of vector lattices. If $X$ is such a lattice, those notions seem - at first glance - intimately related to the lattice operations on $X$.…
We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…
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…
In vector lattices, the concept of a projection band is a basic tool. We deal with projection bands in the more general setting of an Archimedean pre-Riesz space $X$. We relate them to projection bands in a vector lattice cover $Y$ of $X$.…
Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band…
Discovering the underlying structure of a given graph is one of the fundamental goals in graph mining. Given a graph, we can often order vertices in a way that neighboring vertices have a higher probability of being connected to each other.…
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the…
We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and…
Let $X$ be an ordered vector space. The net $\{x_\alpha\}\subseteq X$ is semi unbounded order convergent to $x$ (in symbol $x_\alpha\xrightarrow{suo}x$), if there is a net $\{y_\beta\}$, possibly over a different index set, such that…
Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover $Y$ for a pre-Riesz space $X$, we address the question how to find…
A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of…
In this paper we consider the relationship between order and topology in the vector lattice $C_b(X)$ of all bounded continuous functions on a Hausdorff space $X$. We prove that the restriction of $f\in C_b(X)$ to a closed set $A$ induces an…
For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L, \phi)$ over it, we establish a metric extension result for sections of $L^{\otimes n}$ from a…
We show that for an ideal $H$ in an Archimedean vector lattice $F$ the following conditions are equivalent: $\bullet$ $H$ is a projection band; $\bullet$ Any collection of mutually disjoint vectors in $H$, which is order bounded in $F$, is…
We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which…
The idempotent semigroups (bands) that give rise to partial orders by defining $a \leq b \iff a \cdot b = a$ are the "right-regular" bands (RRB), which are axiomatized by $x\cdot y \cdot x = y \cdot x$. In this work we consider the class of…
We study the electronic structure of an ordered array of poly(para-phenylene) chains produced by surface-catalyzed dehalogenative polymerization of 1,4-dibromobenzene on copper (110). The quantization of unoccupied molecular states is…
It is shown that an ordered vector space $X$ is Archimedean if and only if $\inf\limits_{\tau\in\{\tau\}, y\in L}(x_\tau -y) \ = 0$ for any bounded decreasing net $x_\tau\downarrow$ in $X$, where $L$ is the collection of all lower bounds of…
In this paper, we describe a way of turning a seminormed preordered vector space into an Archimedean order unit space. We show that this construction satisfies a universal property similar to that of the Archimedeanization of Paulsen and…