Polynomial reflexivity in Banach spaces
 Jeff D. Farmer
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We ask when the space ofNhomogeneous 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 upperqestimate, 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.
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 Title
 Polynomial reflexivity in Banach spaces
 Journal

Israel Journal of Mathematics
Volume 87, Issue 13 , pp 257273
 Cover Date
 19940201
 DOI
 10.1007/BF02772998
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Jeff D. Farmer ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Missoure, 65211, Columbia, MO, USA