The Essential Norm of Operators on the Bergman Space.

Analysis Seminar
Wednesday, February 20, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
In this talk, we will characterize the compact operators on Bergman spaces of the ball and polydisc.  The main result we will discuss shows that an operator on the Bergman space is compact if and only if its Berezin transform vanishes on the boundary and additionally this operator belongs to the Toeplitz algebra.  We additionally will comment about how to extend these results to bounded symmetric domains, and for "Bergman-type" function spaces.