Geometry of spaces of real polynomials of degree at most
Christopher Boyd
University College Dublin, IrelandAnthony Brown
University College Dublin, Ireland
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Abstract
We study the geometry of the unit ball of the space of integral polynomials of degree at most on a real Banach space. We prove Smul'yan type theorems for Gâteaux and Fréchet differentiability of the norm on preduals of spaces of polynomials of degree at most . We show that the set of extreme points of the unit ball of the predual of the space of integral polynomials is . This contrasts greatly with the situation for homogeneous polynomials where the set of extreme points of the unit ball is the set .
Cite this article
Christopher Boyd, Anthony Brown, Geometry of spaces of real polynomials of degree at most . Rev. Mat. Iberoam. 33 (2017), no. 4, pp. 1149–1171
DOI 10.4171/RMI/966