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Polynomials on Banach spaces with unconditional bases


Authors: Bogdan C. Grecu and Raymond A. Ryan
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
Published electronically: November 19, 2004
MathSciNet review: 2117209
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Abstract | References | Similar Articles | Additional Information

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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  • 1. A. Defant, J. C. Díaz, D. Garcia, M. Maestre, Unconditional Basis and Gordon-Lewis Constants for Spaces of Polynomials, J. Funct. Anal. 181 (2001), 119-145. MR 1818112 (2002b:46030)
  • 2. S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag, London, 1999.MR 1705327 (2001a:46043)
  • 3. B. R. Gelbaum and J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961), 1281-1286. MR 0147881 (26:5394)
  • 4. S. Kwapien and A. Pe\lczynski, The main triangle projection in matrix spaces and its applications, Studia Math. 34 (1970), 43-68. MR 0270118 (42:5011)
  • 5. M. Matos, On holomorphy in Banach spaces and absolute convergence of Fourier series, Portugal Math. 45 (1988), no. 4, 429-450. (See also Errata: "On holomorphy in Banach spaces and absolute convergence of Fourier series" Port. Math. 47 (1990), no. 1, 13.) MR 0982911 (90f:46075); MR 1079501 (91j:46054)
  • 6. M. Matos and L. Nachbin, Reinhardt domains of holomorphy in Banach spaces, Adv. Math. 92 (1992), no. 2, 266-278. MR 1155467 (93d:46069)
  • 7. P. Meyer-Nieberg, Banach Lattices, Springer Verlag, Berlin, 1991. MR 1128093 (93f:46025)
  • 8. R. A. Ryan, Introduction to Tensor Products of Banach Spaces, Springer Verlag, 2002. MR 1888309 (2003f:46030)
  • 9. H. H. Schaefer, Banach Lattices and Positive Operators, Springer Verlag, New York-Heidelberg, 1974.MR 0423039 (54:11023)

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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

DOI: https://doi.org/10.1090/S0002-9939-04-07738-X
Keywords: Unconditional Schauder basis, homogeneous polynomial, tensor product
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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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