Dokažemo splošen arhimedski izrek o pozitivnosti za hermitske operatorske polinome. Odtod izpeljemo posplošitve Dritschel-Rovnyakove operatorske verzije Fejer-Rieszovega izreka za trigonometrične ...polinome v več spremenljivkah, Ambrozie-Vasilescovega in Scherer-Holovega izreka o pozitivnosti ter sorodnih izrekov. Glavni korak v dokazu je posplošitev abstraktnega arhimedskega izreka o pozitivnosti za algebre z involucijo.
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