Convexity plays an important role in functional analysis, especially in understanding the geometric structure of spaces of operators on a Hilbert space. In this talk, we will discuss the extreme points of some natural convex subsets of B(H), the algebra of bounded linear operators on a Hilbert space H, with particular focus on the closed unit ball and operator intervals arising from an order structure. I will also introduce a quantum (non-commutative) notion of convexity, known as C*- convexity, and examine the corresponding notion of extreme points for certain convex subsets of B(H) within this framework.
Anand O. R is a PhD scholar in the Department of Mathematics at the IIT Madras.
