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Joint Math-Stat Colloquium: Pradipta Bandyopadhyay

Distingushed Speaker from the Indian Statistical Institute


Mathematics/Psychology : 401

Date & Time

May 17, 2024, 11:00 am12:00 pm


TitleOn The Krein-Milman Property in Banach Spaces

AbstractA Banach space X is said to have the Krein-Milman Property (KMP) if every nonempty closed bounded convex set K in X is the closed convex hull of its extreme points.

This property gets its name from the classical Krein-Milman Theorem. It follows that finite dimensional or reflexive spaces have the KMP. 

We give a few examples of Banach spaces without the KMP.

We recall the proof of the Krein-Milman Theorem and show that the proof can be adapted to obtain a sufficient condition for the KMP. 

This sufficient condition is related to the Radon-Nikody'm Property (RNP), which says roughly that the Radon-Nikody'm Theorem holds for vector measures taking values in X. 

We will have the Departmental Coffee and Tea from 10 to 10:45 in M&P 422.