Naj bo ▫$H$▫ separabilen Hilbertov prostor in naj bo ▫${\mathcal B}_{sa}(H)$▫ množica vseh omejenih linearnih sebi-adjungiranih operatorjev. Pravimo, da operatorja ▫$A, B \in {\mathcal B}_{sa}(H)$▫ ...kvazi-komutirata, če obstaja tak neničelni skalar ▫$\xi \in \mathbb{C}$▫, da je ▫$AB=\xi BA$▫. V članku klasificiramo bijektivne preslikave na ▫${\mathcal B}_{sa}(H)$▫, ki ohranjajo kvazi-komutativnost v obeh smereh.
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