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The Quarterly Journal of Mathematics 2005 56(1):53-64; doi:10.1093/qmath/hah022
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© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions please email: journals.permissions@oupjournals.org

Unconditionality in spaces of m-homogeneous polynomials

Andreas Defant1 * and Nigel Kalton2 §

1 Institut of Mathematics, Carl von Ossietzky University, D–26111 Oldenburg, Germany, 2 Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA

Let E be a Banach space with an unconditional basis. We prove that for m ≥ 2 the Banach space P(mE) of all m-homogeneous polynomials on E has an unconditional basis if and only if E is finite dimensional. This answers a problem of S. Dineen.

Received 22 January 2004.

* E-mail: defant{at}mathematik.uni-oldenburg.de

§ E-mail: nigel{at}math.missouri.edu


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