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. https://resolver.caltech.edu/CaltechAUTHORS:20200728-153958382
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Abstract
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.
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| 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]. | ||||||
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| Subject Keywords: | Schatten space; Schur product; Banach algebra; Q-algebra | ||||||
| Issue or Number: | 1 | ||||||
| DOI: | 10.1016/j.jfa.2011.09.001 | ||||||
| Record Number: | CaltechAUTHORS:20200728-153958382 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200728-153958382 | ||||||
| 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, https://doi.org/10.1016/j.jfa.2011.09.001. (http://www.sciencedirect.com/science/article/pii/S0022123611003284) | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 104624 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 28 Jul 2020 22:45 | ||||||
| Last Modified: | 16 Nov 2021 18:33 |
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