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Connes' embedding conjecture and sums of hermitian squares
Klep, Igor, matematik ; Schweighofer, Markus
Dokažemo, da je Connesova domneva o vložitvah von Neumannovih algeber ekvivalentna obstoju določenih algebraičnih certifikatov za sledeč tip pozitivnosti polinoma v nekomutirajočih spremenljivkah: ...sled je nenegativna vselej, kadar spremenljivke nadomestimo s sebi adjungiranimi skrčitvami. Ti algebraični certifikati vsebujejo vsote hermitskih kvadratov in komutatorjev. Pokažemo tudi, da le-ti vselej obstajajo za podoben tip pozitivnosti, kjer namesto matrik vstavljamo elemente separabilnih ▫$II_1$▫-faktorjev.
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