# On Von Neumann’s Inequality

Speaker : Vikramjeet Singh Chandel

Date : 30th September, 2014 (Tuesday)

Time : 09:15 pm – 10:15 pm

Venue : Lecture Hall I, Department of Mathematics

Abstract: In this talk, I would like to present a proof of the Von Neumann’s Inequality. Von Neumann’s inequality says the following: Let $H$ be any Hilbert space and let $T$ be an operator on $H$ such that operator norm of $T$ is less than $1$. Let $P$ be a polynomial in one complex variable, and consider $P(T)$ (replacing $z$ by $T$), which is an operator on $H$. Then the operator norm of $P(T)$ is less than the sup norm of $P$ on the closed unit disc. We, also, will see how we can extend it to Holomorphic functions defined on the unit disc.

Area: Complex Analysis