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Title
Algebraic and continuous properties of multilinear forms

Abstract

Let $X$ be a vector space and let $\phi, \psi \in X^\ast$ be two linear forms on $X.$ It is well known that if, for any $x \in X, $

$$\phi(x) = 0 \Rightarrow \psi(x) = 0,$$

then $\psi = c \phi$ for some scalar $c.$ A continuous version is also known. Namely, if $X$ has a norm, if $||\phi|| = \| \psi \| = 1,$ and if, for any $x \in X,$ with $ \|x\| = 1,$

$$\phi(x) = 0 \Rightarrow |\psi(x)| < \epsilon,$$

then either $||\phi + \psi|| < 2\epsilon$ or $||\phi - \psi|| < 2\epsilon.$


In this talk, we will discuss analogous questions for the case of multilinear forms on a product of spaces, $X_1 \times \cdots \times X_n \to \mathbb{K}.$


(This is joint work with A Cardwell, L. Downey, D. GarcĂ­a, M. Maestre, and I. Zalduendo.)

Speaker(s)
Richard M. Aron (Kent State University, USA)

Date
June 03, 2005

Time
14.30

Room
5.5

 
     
 

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