Israel Journal of Mathematics

, Volume 87, Issue 1, pp 257–273

Polynomial reflexivity in Banach spaces

  • Jeff D. Farmer

DOI: 10.1007/BF02772998

Cite this article as:
Farmer, J.D. Israel J. Math. (1994) 87: 257. doi:10.1007/BF02772998


We ask when the space ofN-homogeneous analytic polynomials on a Banach space is reflexive. This turns out to be related to whether polynomials are weakly sequentially continuous, and to the geometry of spreading models. For example, if these spaces are reflexive for allN, no quotient of the dual space may have a spreading model with an upperq-estimate, and every bounded holomorphic function on the unit ball has a Taylor series made up of weakly sequentially continuous polynomials (we assume the approximation property). Alencar, Aron and Dineen [AAD] gave the first example of some properties of a polynomially reflexive space (usingT*, the original Tsirelson space); we show that these properties and others are shared by all polynomially reflexive spaces.

Copyright information

© Hebrew University 1994

Authors and Affiliations

  • Jeff D. Farmer
    • 1
  1. 1.Department of MathematicsUniversity of MissoureColumbiaUSA

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