The projection constant for the trace class
We study the projection constant of the space of operators on n-dimensional Hilbert spaces with the trace norm S 1 (n).We show an integral formula for the projection constant of S 1 (n); namely, (S 1 (n)) = n U n |tr(U )| dU , where the integration is with respect to the Haar probability measure on the group U n of unitary operators.Using a probabilistic approach, we derive the limit formula lim n (S 1 (n))/n = /2.
Authors
- Andreas Defant
- Mieczysław Mastyło (ORCID: https://orcid.org/0000-0003-2019-2284)
- Marcelo Vásquez Mansilla (ORCID: https://orcid.org/0000-0002-3829-7722)
- Santiago Muro (ORCID: https://orcid.org/0000-0002-0394-8716)
- Daniel Galicer (ORCID: https://orcid.org/0000-0001-6513-5844)
Institutions
- Carl von Ossietzky Universität Oldenburg (DE)
- Universidad de Buenos Aires (AR)
- National University of Rosario (AR)
- Fundación Ciencias Exactas y Naturales (AR)
- Adam Mickiewicz University in Poznań (PL)
Publication Details
- Journal
- Analysis & PDE
- Published
- 2025-02-05
- DOI
- https://doi.org/10.2140/apde.2025.18.527
- Citations
- 2
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 3.01
Funders
- Consejo Nacional de Investigaciones Científicas y Técnicas