Mathematics Colloquium

Professor Hamza El Azhar
On the subnormal Aluthge transform of weighted shifts


For recursively generated shifts, we present recent definitive answers about the possible equivalence of two outstanding problems in the theory of unilateral weighted shifts: 

1) The Subnormality Problem: When is the Aluthge transform of a subnormal weighted shift still subnormal?

2) The Square Root Problem: When does a nonnegative Berger measure admit a nonnegative square root (for the convolution product)? 

For atomic measures with at most 6 atoms, our main result provides a new analytic proof to recover known results on the equivalence of the two problems. 

Subsequently, we obtain an example of a 7--atomic measure for which the equivalence fails.  This provides a negative answer to a conjecture related to the above-mentioned equivalence.



*The Math Colloquium will be available live via Zoom at and recordings of the sessions will be available at usually within a couple hours of the colloquium finishing.


Fyi.: We usually gather on colloquium Thursdays at 2:30 pm in the common room, Muhly lounge, so folks can meet the speaker.

And after the talk we also plan colloquium dinner, usually at 6:30 pm. Everyone is welcome to all the colloquium events.

Event Date: 
April 18, 2024 - 3:30pm
213 MLH and Online (See URL)
Calendar Category: