The interactions between operator theory and complex analysis of one variable are now well known but are still an active _eld of research. The theory of truncated Toeplitz operators is a nice illustration of these interactions. In this project we will study the paper of Donald Sarason titled by Algebraic Properties of Truncated Toeplitz Operators.
The operators of the paper's title are compression of multiplication operators to proper invariant subspace of the bakward shift operator on H2. The paper inspired much subsequent work because of the questions are raised.