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The unit ball of the complex P(H-3)

Grecu, B.C. and Muñoz-Fernández, Gustavo Adolfo and Seoane Sepúlveda, Juan Benigno (2009) The unit ball of the complex P(H-3). Mathematische Zeitschrift, 263 . pp. 775-785. ISSN 0025-5874

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Let H be a two-dimensional complex Hilbert space and P(H-3) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, B-P(3H), from which we deduce that the unit sphere of P(H-3) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of B-P(3H) remains extreme as considered as an element of B-L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(H-3) and give a characterization of its smooth points.

Item Type:Article
Uncontrolled Keywords:Unconditional constant; Polynomial inequalities; Trinomials; Homogeneous polynomials; Extreme points
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16965

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