Naslov: Maps on self-adjoint operators preserving numerical range of products up to a factor He, Kan (Avtor)Hou, Jin Chuan (Avtor)Dolinar, Gregor (Avtor)Kuzma, Bojan (Avtor) http://www.actamath.com/Jwk_sxxb_cn/CN/volumn/volumn_1986.shtml Neznan jezik Delo ni kategorizirano 1.01 - Izvirni znanstveni članek IAM - Inštitut Andrej Marušič Let ▫$H$▫ 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 ▫$A in {mathscr{S}}_a(H)$▫. matematika, teorija operatorjev, numerični zaklad, ohranjevalci 2011 str. 925-932 Vol. 54, no. 6 0583-1431 517.983 16397401 1726 26 Gradivo ni uvrščeno v področja.

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## Sekundarni jezik

Jezik: Angleški jezik Let ▫$H$▫ 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 ▫$$W(AB - \xi BA) = W(\Phi(A)\Phi(B) - \eta\Phi(B)\phi(A))$$▫ 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 ▫$A \in {\mathscr{S}}_a(H)$▫. matematika, teorija operatorjev, numerični zaklad, ohranjevalci, mathematics, operator theory, numerical range, preservers, product up to a factor

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