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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Polynomials on Banach spaces with unconditional bases
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by Bogdan C. Grecu and Raymond A. Ryan PDF
Proc. Amer. Math. Soc. 133 (2005), 1083-1091 Request permission

Abstract:

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.
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Additional Information
  • Bogdan C. Grecu
  • Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
  • Email: bogdan@wuzwuz.nuigalway.ie
  • Raymond A. Ryan
  • Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
  • Email: ray.ryan@nuigalway.ie
  • Received by editor(s): November 19, 2003
  • Published electronically: November 19, 2004
  • Additional Notes: The first author acknowledges the support of a Postdoctoral Fellowship funded by Enterprise Ireland.
    The second author acknowledges the support of a Basic Research Grant from Enterprise Ireland.
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1083-1091
  • MSC (2000): Primary 46B15, 46G20; Secondary 46B42, 46B28
  • DOI: https://doi.org/10.1090/S0002-9939-04-07738-X
  • MathSciNet review: 2117209