Friday, October 9, 2015 3:30 pm
-
3:30 pm
EDT (GMT -04:00)
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