October 16:  Jani Virtanen, CIMS

Toeplitz operators on Bergman spaces
  

  The Bergman space $A^2$ consists of all analytic functions in the open unit disk that are square-summable. As $A^2$ is a closed subspace of $L^2$, there is a projection $P$ of $L^2$ onto $A^2$. The Toeplitz operator $T_a$ with symbol $a$ is the operator acting on $A^2$ of multiplication by the function $a$ followed by the orthogonal projection $P$. I discuss boundedness, compactness and spectral properties of Toeplitz operators on Bergman spaces.