Daugavet’s equation and Jordan elementary operators

The aim of this paper is to investigate the Daugavet equation for a Jordan elementary operator. More precisely, we study the equation ‖ I + U J , A , B ‖ = 1 + 2 ‖ A ‖ ‖ B ‖ , where I stands for the identity operator, A and B are two bounded operators acting on a complex Hilbert space H , J is a nor...

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Bibliographic Details
Published in:Advances in operator theory 2024-07, Vol.9 (3), Article 42
Main Authors: Taki, Zakaria, Kaadoud, Mohamed Chraibi, Guesba, Messaoud
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
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Summary:The aim of this paper is to investigate the Daugavet equation for a Jordan elementary operator. More precisely, we study the equation ‖ I + U J , A , B ‖ = 1 + 2 ‖ A ‖ ‖ B ‖ , where I stands for the identity operator, A and B are two bounded operators acting on a complex Hilbert space H , J is a norm ideal of operators on H , and U J , A , B is the restriction of the Jordan operator U A , B to J . In the particular case where J = C 2 ( H ) is the ideal of Hilbert–Schmidt operators, we give necessary and sufficient conditions under which the above equation holds.
ISSN:2662-2009
2538-225X
DOI:10.1007/s43036-024-00342-9