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

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http://www.springerlink.com | Publisher |

## Abstract

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 |
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Uncontrolled Keywords: | Unconditional constant; Polynomial inequalities; Trinomials; Homogeneous polynomials; Extreme points |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16965 |

Deposited On: | 05 Nov 2012 11:26 |

Last Modified: | 28 Nov 2016 09:30 |

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