Hall 123

Continuous function calculus and its applications

Bipul Saurabh

IMSc, Chennai

Given a normal operator T and a polynomial p, the operator p(T) can be defined naturally.
Can we extend this to more general functions? In particular, for a holomorphic function or
a continuous function f , can we define f(T) in a “natural“ manner. For example, does the operator sin(e^(− d/dx)) make sense? To answer this, we will introduce some function calculi, in particular, continuous function calculus. If time allows, we will see some of their applications and
discuss their connection to other concepts in operator algebra and non-commutative geometry.