Maps on self-adjoint operators preserving numerical range of products up to a factor

He, Kan; Hou, Jin Chuan; Dolinar, Gregor; Kuzma, Bojan

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Title:	Maps on self-adjoint operators preserving numerical range of products up to a factor
Authors:	ID He, Kan (Author) ID Hou, Jin Chuan (Author) ID Dolinar, Gregor (Author) ID Kuzma, Bojan (Author)
Files:	http://www.actamath.com/Jwk_sxxb_cn/CN/volumn/volumn_1986.shtml
Language:	Unknown
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	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 $A in {mathscr{S}}_a(H)$ .
Keywords:	matematika, teorija operatorjev, numerični zaklad, ohranjevalci
Year of publishing:	2011
Number of pages:	str. 925-932
Numbering:	Vol. 54, no. 6
PID:	20.500.12556/RUP-7742
ISSN:	0583-1431
UDC:	517.983
COBISS.SI-ID:	16397401
Publication date in RUP:	03.04.2017
Views:	3024
Downloads:	37
Metadata:
:	HE, Kan, HOU, Jin Chuan, DOLINAR, Gregor and KUZMA, Bojan, 2011, Maps on self-adjoint operators preserving numerical range of products up to a factor. [online]. 2011. Vol. 54, no. 6, p. 925–932. [Accessed 3 April 2025]. Retrieved from: http://www.actamath.com/Jwk_sxxb_cn/CN/volumn/volumn_1986.shtml Copy citation

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Secondary language

Language:	English
Abstract:	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 $A \in {\mathscr{S}}_a(H)$ .
Keywords:	matematika, teorija operatorjev, numerični zaklad, ohranjevalci, mathematics, operator theory, numerical range, preservers, product up to a factor

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