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# Operator Algebra Seminars

**
Fri., Oct. 28, 2016 10:00 a.m.
- Fri., Oct. 28, 2016 12:00 p.m.
**

**
Location: RIC 215
**

**Speaker:** Samir Raouafi

**Title:** Numerical Range and Mapping Theorems, III

**Abstract:**

The numerical range of an operator A is a remarkable region of the complex plane. It captures information about the spectrum and the behavior of A.

In this third lecture, I will introduce spectral sets and discuss some important properties related to special classes of operators and the numerical range of an arbitrary operator. Moreover, we will discuss Crouzeix's conjecture which is that the numerical range of any square matrix A is a 2-spectral set for A.