Generalized bicircular projections via rank preserving maps on the spaces of symmetric and antisymmetric operators

Abstract

V članku so obravnavane naslednje, med seboj povezane, preslikave na simetričnih in antisimetričnih operatorjih, ki delujejo na kompleksnem Hilbertovem prostoru: linearni ohranjevalci ranga ena na simetričnih operatorjih, linearni ohranjevalci ranga dva na antisimetričnih operatorjih, surjektivne linearne izometrije in posplošeni bicirkularni projektorji.We study several related maps from the space of symmetric (respectively, antisymmetric) operators, acting on a complex Hilbert space, to itself: rank preserving linear maps (more precisely, maps preserving rank one operators in the symmetric case, and maps preserving rank two operators in the antisymmetric case), surjective linear isometries and generalized bicircular projections