Naslov (srp)

Majorizacione relacije i stohastički operatori na diskretnim Lebegovim prostorima

Autor

Ljubenović, Martin Z. 1985-

Doprinosi

Đorđević, Dragan 1970-
Petković, Ljiljana 1953-
Živković-Zlatanović, Snežana 1965-
Mosić, Dijana 1981-
Radović, Ljiljana 1969-

Opis (srp)

Biobibliografski podaci: str. [129-130] Datum odbrane: 23.03.2017. Functional analysis

Opis (eng)

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.

Jezik

srpski

Datum

2016

Licenca

Ovo delo je licencirano pod uslovima licence
Creative Commons CC BY-NC-ND 2.0 AT - Creative Commons Autorstvo - Nekomercijalno - Bez prerada 2.0 Austria License.

http://creativecommons.org/licenses/by-nc-nd/2.0/at/legalcode