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Ljubenović, Martin Z. 1985
Majorizacione relacije i stohastički operatori na diskretnim Lebegovim prostorima
AutorstvoNekomercijalnoBez prerade 3.0 Srbija (CC BYNCND 3.0)
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Academic metadata
Doktorska disertacija
Prirodnomatematičke nauke

Univerzitet u Nišu
Prirodnomatematički fakultet
Odsek za matematiku i informatiku
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Majorization relations and stochastic operators on discrete Lebesgue spaces
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 preorders, 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.
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 preorders, 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.