Related papers: Boolean Methods in the Theory of Vector Lattices
This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.
This is a brief overview of the basic techniques of Boolean valued analysis.
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities.
The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector…
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
Lattice induced threshold function is a Boolean function determined by a particular linear combination of lattice elements. We prove that every isotone Boolean function is a lattice induced threshold function and vice versa. We also…
This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for…
The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact…
We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the equivalence of orthosymmetry and orthogonal additivity.
A Vitali-type theorem for vector lattice-valued modulars with respect to filter convergence is proved. Some applications are given to modular convergence theorems for moment operatorsin the vector lattice setting, and also for the Brownian…
In this paper, we will study on some topologies induced by order convergences in a vector lattice. We will investigate the relationships of them.
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a…
The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space geomtry.
A new way of describing massive vector bosons is proposed. It is possible to change the boson propagator in such way that the theory with the vector boson interaction becomes a renormalized one. One example of the efficacy of such a…
We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…