The Schatten space $S_4$ is a $Q$-algebra
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- by Christian Le Merdy PDF
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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.References
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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
- MR Author ID: 308170
- Email: lemerdy@math.univ-fcomte.fr
- Received by editor(s): June 26, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 715-719
- MSC (1991): Primary 47D25; Secondary 47A80, 46B70
- DOI: https://doi.org/10.1090/S0002-9939-98-04545-6
- MathSciNet review: 1468194