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The commuting graph of bounded linear operators on a Hilbert space
Ambrozie, Calin ...
Konstruiran je takšen operator ▫$T$▫ na neskončno dimenzionalnem separabilnem Hilbertovem prostoru, za katerega velja, da je komutant vsakega operatorja, ki ni skalarni večkratnik identičnega ...operatorja in ki komutira s ▫$T$▫, sovpada s komutantom operatorja ▫$T$▫. Po drugi strani pa je za veliko razredov operatorjev pokazano, da lahko najdemo takšno končno zaporedje operatorjev, pri čemer je prvi člen zaporedja dani operator, zadnji člen zaporedja pa je idempotent ranga ena, tako da sosednja operatorja v zaporedju komutirata. Razredi, ki jih študiramo so: operatorji končnega ranga, normalni operatorji, parcialne izometrije in ▫$C_0$▫ kontrakcije. Pokazano je, da za vsako množico da/ne pogojev med točkami v neki končni množici obstajajo takšni operatorji nakončno dimenzionalnem Hilbertovem prostoru, da njihove medsebojne komutativnostne relacije natanko ustrezajo danim da/ne pogojem.
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