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Dvoretzky's theorem: some applications and some ideas

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If you have a question about this talk, please contact Josephine Evans.

Dvoretzky’s theorem was a major landmark in the local theory of Banach spaces. Very roughly it says that every infinite-dimensional Banach space contains slices that look like finite dimensional Hilbert space.

Although the proof is involved, we will look at some simple cases and deduce the theorem here. We will also give some results as to why such a theorem is of interest. No familiarity with Banach space theory will be assumed, and the talk will be aimed at people with a basic knowledge of functional analysis.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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