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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Schatten space $S_{4}$ is a $Q$-algebra


Author: Christian Le Merdy
Journal: Proc. Amer. Math. Soc. 126 (1998), 715-719
MSC (1991): Primary 47D25; Secondary 47A80, 46B70
MathSciNet review: 1468194
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Abstract: For any $1 \leq p \leq \infty $, let $S_{p}$ denote the classical $p$-Schatten space of operators on the Hilbert space $\ell _{2}$. It was shown by Varopoulos (for $p \geq 2$) and by Blecher and the author (full result) that for any $1 \leq p \leq \infty , S_{p}$ equipped with the Schur product is an operator algebra. Here we prove that $S_{4}$ (and thus $S_{p}$ for any $2 \leq p \leq 4$) is actually a $Q$-algebra, which means that it is isomorphic to some quotient of a uniform algebra in the Banach algebra sense.


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Additional Information

Christian Le Merdy
Affiliation: Equipe de Mathématiques, Université de Franche-Comté, CNRS UMR 6623, F-25030 Besancon Cedex, France
Email: lemerdy@math.univ-fcomte.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04545-6
PII: S 0002-9939(98)04545-6
Received by editor(s): June 26, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society