Unbounded Toeplitz operators (Q939146)

The author presents the basic theory of unbounded Toeplitz operators on the Hardy space \(H^2\) of the unit disc. This includes a brief review about unbounded Toeplitz operators with \(L^2\) symbols, preliminary material on the Smirnov class and de Branges-Rovnyak spaces, and then properties of analytic and coanalytic Toeplitz operators. Compressions of unbounded Toeplitz operators to invariant subspaces of the backward shift on \(H^2\) are also studied. The paper ends by stating some open questions.