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

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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. © 2011 Elsevier Inc.

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Briët, J., Buhrman, H., Lee, T., & Vidick, T. (2012). All Schatten spaces endowed with the Schur product are Q-algebras. Journal of Functional Analysis, 262(1), 1–9. https://doi.org/10.1016/j.jfa.2011.09.001

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