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13.
A note on equivalence preserving maps
Petek, Tatjana ; Radić, Gordana
Naj bo ▫$\mathcal{B(X)}$▫ algebra vseh omejenih linearnih operatorjev na kompleksnem Banachovem prostoru ▫$\mathcal{X}$▫. Z ▫$A\sim B$▫, ▫$A, B \in \mathcal{B(X)}$▫, označimo relacijo ▫$B=TAS$▫ za ...neka obrnljiva operatorja ▫$T, S \in \mathcal{B(X)}$▫. Podali bomo natančen opis surjektivnih preslikav ▫$\phi: \mathcal{B(X)} \to \mathcal{B(X)}$▫, za katere pri poljubnih ▫$A$▫, ▫$B$▫, ▫$C \in \mathcal{B(X)}$▫ velja, da je ▫$A - B \sim C$▫ natanko tedaj ko je ▫$\phi(A) - \phi(B) \sim \phi(C)$▫.
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