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All Schatten spaces endowed with the Schur product are Q-algebras

Briët, Jop and Buhrman, Harry and Lee, Troy and Vidick, Thomas (2012) All Schatten spaces endowed with the Schur product are Q-algebras. Journal of Functional Analysis, 262 (1). pp. 1-9. ISSN 0022-1236. doi:10.1016/j.jfa.2011.09.001.

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We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of Pérez-García for the trace class, this completes the answer to a long-standing question of Varopoulos.

Item Type:Article
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Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2011 Elsevier Inc. Published by Elsevier Inc. Received 8 April 2011, Accepted 1 September 2011, Available online 26 September 2011. Supported by a Vici grant from the Dutch Science Foundation (NWO) and EU-grant QCS. We thank the anonymous referee for helpful comments. J.B. thanks David Pérez-García and Ronald de Wolf for useful comments on earlier versions of this manuscript, Carlos Palazuelos for helpful suggestions and Carlos González Guillén for providing the reference [15].
Funding AgencyGrant Number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Subject Keywords:Schatten space; Schur product; Banach algebra; Q-algebra
Issue or Number:1
Record Number:CaltechAUTHORS:20200728-153958382
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Official Citation:Jop Briët, Harry Buhrman, Troy Lee, Thomas Vidick, All Schatten spaces endowed with the Schur product are Q-algebras, Journal of Functional Analysis, Volume 262, Issue 1, 2012, Pages 1-9, ISSN 0022-1236, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104624
Deposited By: Tony Diaz
Deposited On:28 Jul 2020 22:45
Last Modified:16 Nov 2021 18:33

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