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Mappings preserving the idempotency of products of operators
Petek, Tatjana
Dobimo splošno obliko surjektivne (brez predpostavke aditivnosti) preslikave ▫$\phi$▫, ki ohranja neničelno idempotentnost nekaterih produktov, definirane na (a) algebri vseh omejenih linearnih ...operatorjev ▫$B(X)$▫, kjer je ▫$X$▫ vsaj trirazsežen realen ali kompleksen vektorski prostor, (b) na množici vseh idempotentnih operatorjev ranga 1 v ▫$B(X)$▫ in (c) na množici vseh idempotentnih operatorjev v ▫$B(X)$▫. V vsakem od teh primerov se izkaže, da je ▫$\phi$▫ aditivna in bodisi multiplikativna bodisi antimultiplikativna.
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