Open AccessОграниченные ортоморфизмы между локально солидными векторными решетками
Author(s) -
R. Sabbagh,
Omid Zabeti
Publication year - 2021
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/c1197-8093-8231-u
Subject(s) - bounded function , mathematics , pure mathematics , lattice (music) , lebesgue integration , class (philosophy) , property (philosophy) , discrete mathematics , computer science , mathematical analysis , physics , philosophy , epistemology , artificial intelligence , acoustics
The main aim of the present note is to consider bounded orthomorphismsbetween locally solid vector lattices. We establish a version of the remarkableZannen theorem regarding equivalence between orthomorphisms and the underlyingvector lattice for the case of all bounded orthomomorphisms. Furthermore, weinvestigate topological and ordered structures for these classes of orthomorphisms,as well. In particular, we show that each class of bounded orthomorphismspossesses the Levi or the $AM$-properties if and only if so is the underlyinglocally solid vector lattice. Moreover, we establish a similar result for theLebesgue property, as well.