## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, October 9, 2015 — 3:30 PM EDT

**Javad Mashreghi, Laval University**

"The Halmos Conjecture on the Numerical Range"

Let $T$ be an operator on a Hilbert space $H$ with numerical radius $w(T)

\leq 1$. Halmos conjectured that $w(T^n) \leq 1$, $n \geq 1$. After

several partial results, it was finally settled by Berger using dilation

theory. The Berger--Stampfli theorem, a generalization of the conjecture,

says that if $f$ is a function in the disk algebra such that $f(0)=0$,

then $w(f(T))\leq \|f\|_\infty$. We give an elementary proof of this

result using finite Blaschke products.

Joint work with H. Klaja and T. Ransford.

MC 5417

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1