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The projection
constant for the trace class
Andreas Defant, Daniel Galicer, Martin Mansilla, Mieczysław Mastyło and Santiago Muro |
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Vol. 18 (2025), No. 2, 527–548
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Abstract |
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We study the projection constant of the space of operators on -dimensional Hilbert spaces with the trace norm . We show an integral formula for the projection constant of ; namely, , where the integration is with respect to the Haar probability measure on the group of unitary operators. Using a probabilistic approach, we derive the limit formula . |
Keywords
projection constant, trace class operators, harmonics,
local invariants in Banach spaces
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Mathematical Subject Classification
Primary: 46B06, 46B07, 47B10
Secondary: 33C55, 43A15, 46G25
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Milestones
Received: 29 May 2023
Accepted: 18 February 2024
Published: 5 February 2025
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Authors |
| Andreas Defant | |
| Institut für Mathematik Carl von Ossietzky Universität Oldenburg Oldenburg Germany |
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| Daniel Galicer | |
| Departamento de Matemática Universidad de Buenos Aires and IMAS-CONICET Ciudad Universitaria Buenos Aires Argentina |
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| Martin Mansilla | |
| Departamento de Matemática Universidad de Buenos Aires and IMAS-CONICET Ciudad Universitaria Buenos Aires Argentina |
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| Mieczysław Mastyło | |
| Faculty of Mathematics and Computer
Science Adam Mickiewicz University in Poznań Poznań Poland |
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| Santiago Muro | |
| Facultad de Cs. Exactas, Ingenieria
y Agrimensura Universidad Nacional de Rosario and CIFASIS-CONICET Rosario Argentina |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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