Maps on self-adjoint operators preserving numerical range of products up to a factorHe, Kan (Avtor) Hou, Jin Chuan (Avtor) Dolinar, Gregor (Avtor) Kuzma, Bojan (Avtor) matematikateorija operatorjevnumerični zakladohranjevalciLet ▫$H$▫ be a complex Hilbert space and ▫${mathscr{S}}_a(H)$▫ the space of all self adjoint operators on ▫$H$▫. ▫$Phi colon {mathscr{S}}_a(H) to {mathscr{S}}_a(H)$▫ is a surjective map. For ▫$xi, eta in mathbb{C} setminus {1}$▫, then ▫$Phi$▫ satisfies that ▫$$W(AB - xi BA) = W(Phi(A)Phi(B) - etaPhi(B)phi(A))$$▫ for all ▫$A,B in {mathscr{S}}_a(H)$▫ if and only if there exists a unitary operator or con-unitary operator ▫$U$▫ such that ▫$Phi(A) = UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫ or ▫$Phi(A) = -UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫.20112016-04-08 16:48:42Delo ni kategorizirano7742ISSN: 0583-1431UDK: 517.983OceCobissID: 24853760COBISS.SI-ID: 16397401sl