o:1345 Majorizacione relacije i stohastički operatori na diskretnim Lebegovim prostorima Majorization relations and stochastic operators on discrete Lebesgue spaces : doctoral dissertation sr In this dissertation, notions of weak majorization and weak supermajorization on descrete Lebesgue spaces are introduced, using doubly substochastic and superstochastic operators. We generalize very important results from finite dimenstional majorization theory, which give close relationships between standard and mentioned weak majorizations and corresponding stochastic operators. It is proved that all three majorization relations are pre-orders, and if we identify all functions which are different up to the permutation, or up to the partial permutation for weak majorization case, these relations may be considered as parial orders. The complete characterisation of linear preservers of weak majorization and weak supermajorization, has been carried out. It was observed that an arbitrary positive preserver one of investigated majorization, preserves the remaining two relations. It was provided that there are two different forms of linear preservers of weak majorization on discrete Lebesgue spaces lp(I), when p is greater than 1 and when p is equal 1. The notion of majorization on the set of all doubly stochastic operators is extended. Kakutani’s conjecture is restated and sufficient conditions that this conjecture is true are given. Biobibliografski podaci: str. [129-130] Datum odbrane: 23.03.2017. Functional analysis 1025444841 91552101 5094 91552100 1025444841 2017-06-29T16:42:00.053Z 45 no 46 mentor Martin Z. 1985- Ljubenović 2016 63 mentor Dragan 1970- Đorđević 2016 63 član komisije Ljiljana 1953- Petković 2016 63 član komisije Snežana 1965- Živković-Zlatanović 2016 63 član komisije Dijana 1981- Mosić 2016 63 član komisije Ljiljana 1969- Radović 2016 127 str. 2192330 http://phaidrabg.bg.ac.rs/o:1345 no yes 4 2017-06-29T16:42:00.320Z 70 stohastički operatori, majorizacione relacije, permutacija,diskretni Lebegovi prostori stochastic operators, majorization relations, permutation, discreteLebesgue spaces 517.983.23(043.3) 517.521(043.3) 512.64/.643(043.3) 1738 18A07 18A0701 2016