Cilj tega diplomskega dela je predstaviti reprezentacijo Banachovih mrež s krepko enoto s prostori funkcij C(K) na kompaktnih topoloških prostorih K. V ta namen je vpeljan pojem Boolove algebre in dokazan Stoneov reprezentacijski izrek, ki služi kot močno orodje pri reprezentaciji Banachovih mrež. Nato je definiran Rieszov prostor, ki je vektorski ...
Published in Mathematical Notes
Abstract Regular multilinear operators and regular homogeneous polynomials acting between Banach lattices are automatically continuous, but the converse, in general, is not true. The problem arises of characterizing Banach lattices for which the classes of continuous and regular multilinear operators (or homogeneous polynomials) coincide. The aim o...
Published in Lobachevskii Journal of Mathematics
AbstractIn this article we explore orthogonally additive (nonlinear) operators in vector lattices. First we investigate the lateral order on vector lattices and show that with every element \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...
Published in Mathematical Notes
Abstract The first example of a Banach space with the approximation property but without the bounded approximation property was given by Figiel and Johnson in 1973. We give the first example of a Banach lattice with the approximation property but without the bounded approximation property. As a consequence, we prove the existence of an integral ope...
In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach space variant of it. Some results are generalized to the case of Banach lattices on 0,𝑏],0Sofia University SRF, Grant/Award Number:80-10-13/2018
We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the $q$-convexity of the Banach lattice.
Published in Mathematica Slovaca
In the present paper we introduce generalized vector-valued Musielak-Orlicz sequence space l(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators of s-type and operator ideals by using the sequence of s-number (in the sense of Pietsch) under cer...
Published in Siberian Mathematical Journal
We consider a new class of narrow orthogonally additive operators in lattice-normed spaces and prove the narrowness of every C-compact norm-laterally-continuous orthogonally additive operator from a Banach–Kantorovich space V into a Banach space Y. Furthermore, every dominated Urysohn operator from V into a Banach sequence lattice Y is also narrow....
Published in Archiv der Mathematik
Let E and F be Banach lattices. We show first that the disjointness preserving linear functionals separate the points of any infinite dimensional Banach lattice E, which shows that in this case the unbounded disjointness preserving operators from E→F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
Published in Mathematical Notes
The objective of this paper is to present a survey of the main results concerning the domination problem for operators in Banach lattices, to lay down a general approach to the study of the problem, and to indicate several directions for further investigations.
