# On Numerical Range and Numerical Radius of a Bounded Operator.

Date : 25 November, 2014 (Tuesday)

Time : 09:15 pm – 10:15 pm

Venue : Lecture Hall I, Department of Mathematics

Abstract: First comes a bounded operator $A$ on a Hilbert space $H$, then a numerical valued map on $A$ defined by $h\longrightarrow$, where the notation on the RHS denotes the inner product on the Hilbert space $H$. The “numerical range” is the Range of the numerical valued map defined above restricted to the unit sphere of the Hilbert space $H$. This subset of the complex plane turned out to be a main object of interest to several mathematicians. We shall discuss several nice properties of this subset. The “numerical radius” is defined to be the maximum modulus of the elements in numerical range. It turns out that this defines a norm on the algebra of bounded operators. We shall discuss some properties of this norm too.

Area: Functional Analysis