On approximate versions of reducibility results for matrix groups and semigroups
Kuzma, Bojan, 1968- ...
Funkcijo ▫$k$▫ spremenljivk imenujemo razcepnostna za multiplikativno polgrupo ▫$\mathcal{S} \subseteq M_n(\mathbb{C})$▫, če je polgrupa razcepna, čim ▫$f$▫ uniči vse njene elemente . V članku za ...vsako zvezno razcepnostno funkcijo na podgrupah unitarnih matrik pokažemo, da je podgrupa razcepna kadar je ▫$f$▫ na njej enakomerno dovolj blizu 0. Podane so tudi razširitve tega rezultata za nekatere vrste polgrup. Dobljeni rezultati vsebujejo in razširjajo številne znane rezultate te vrste. V posebnem je dokazano,, da je podgrupa kompleksnih unitarnih matrik razcepna, če je modul vseh njenih elementov na fiksni nediagonalni poziciji▫ $(i, j)$▫ dovolj majhen.
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