Abstract:
This thesis contains results about the matrix valued truncated Toeplitz operators
(MTTO's) de ned on the model space K = H2 H2(E), with a xed pure
inner function and E an arbitrary Hilbert space. The class of MTTO's is denoted by
T (K ). In the main work of this thesis we shall concern with the extension of some
of the results obtained in the scalar case by D. Sarason in [27].
After gathering together the mathematical preliminaries of this work in Chapter
1, in Chapter 2 we shall present the most important properties of the model spaces
K and some very important operators S and S
in T (K ). The main object of this
thesis is the study of the matrix generalization of the truncated Toeplitz operators
introduced in [27]; a more recent presentation is [17]. This will be the content of
Chapter 3, 4, 5. Finally, in Chapter 6 the preceding theory is applied to initiate the
study of nite rank operators in T (K ).
