Halmos Mathematics Colloquium Series Hosted Talk on Numerical Ranges

On Thursday, January 17, Ilya Spitkovsky, Ph.D., Professor of Mathematics, New York University Abu Dhabi, presented a talk entitled, “On some generalizations of the numerical range and their properties”.

The seminar was about For a bounded linear operator A (or, in the finite dimensional setting, an n-by-n matrix A) its classical numerical range is defined as the mage of the unit sphere under the mapping f(x)=(Ax,x). The normalized numerical range results when in this definition (Ax,x) is replaced by (Ax,x)/||Ax||.  They also discussed some general properties of this set, and in particular provide its complete description in the cases when A is normal or n=2.

Halmos College of Natural Sciences and Oceanography department of mathematics hosts the mathematics colloquium series in the Parker Building, Room 301.