20.500.12556/RUP-7742 Maps on self-adjoint operators preserving numerical range of products up to a factor 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 ▫$A in {mathscr{S}}_a(H)$▫. 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 matematika teorija operatorjev numerični zaklad ohranjevalci mathematics operator theory numerical range preservers product up to a factor true true false Neznan jezik Angleški jezik Delo ni kategorizirano 2016-04-08 16:48:42 2017-04-03 08:10:58 2024-03-01 13:33:26 0000-00-00 00:00:00 2011 0 0 str. 925-932 no. 6 Vol. 54 2011 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0583-1431 517.983 24853760 16397401 http://www.actamath.com/Jwk_sxxb_cn/CN/volumn/volumn_1986.shtml 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7742 Inštitut Andrej Marušič 0 0 0