turkmath.org

The closed subspaces of the Hardy-Hilbert space of the unit disc which are invariant under the backward shift are called model spaces. These spaces were defined and investigated by Sarason and DeBranges in 70`s. Operator theory in particular theory of Toeplitz operators on these spaces was begun by the paper "On Algebraic Properties of Truncated Toeplitz Opeartors" of Sarason which was published in 2007 and became popular in the last two decades. In this expository talk I aim to investigate the theory of truncated toeplitz operators with special emphasis on structure of C*-algebras generated by these operators which is the main result of Garcia and Ross. The talk aims to attract young researchers, in particular graduate students, into this very interesting field of Operator Theory.