Majorizacione relacije i stohastički operatori na diskretnim Lebegovim prostorima
Ljubenović, Martin Z.
Faculty:University of Niš, Faculty of Science and Mathematics
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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.View More
Keywords:stohastički operatori; stochastic operators; majorization relations; permutation; discrete Lebesgue spaces; majorizacione relacije; permutacija; diskretni Lebegovi prostori