C. Boyd

will speak on

Real Extreme points of Spaces of Complex Polynomials

Time: 4:00PM
Date: Tue 7th November 2017
Location: SCN 125 [map]

Abstract: Given a Banach space $E$ and a positive integer $n$ we let $\mathcal P_I(^nE)$
denote the space of all $n$-homogeneous integral polynomials on $E$. This space
generalise the trace class operators and plays an important role in the
duality theory of spaces of homogeneous
polynomials. When $E$ is a real Banach space and $n\ge 2$ it is known that the
set of extreme points of the unit ball of $\mathcal P_I(^nE)$ is equal to the set
$\lbrace\pm\varphi^n:\|\varphi\|=1\rbrace$. When $E$ is a complex Banach space a
characterisation of the set of extreme points of the unit ball of $\mathcal P_I(^nE)$ is not so easy
to establish. In this talk, I will look at what can be said for low values of
$n$ and small linear combinations of extreme points. This is joint work with
Anthony Brown.

(This talk is part of the Analysis series.)

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