Date of Award
Program or Major
Doctor of Philosophy
The de Branges-Rovnyak spaces have been introduced by Louis de Branges and James Rovnyak, and have been studied by several authors, in particular by Donald Sarason. The object of this thesis is to study more extensively some properties of this class of spaces. In particular, which of these spaces are invariant under the action of which composition operators, or adjoints of composition operators.
Some known facts and a couple of new properties are included in Chapter 1. There it is shown that the norm of the kernel function for evaluation at a point in the unit disc (in the de Branges space) equals the operator norm of a certain multiplication operator. It is also shown that the de Branges space defined using an inner function is finite dimensional if and only if the inner function is continuous.
The second chapter contains conditions that assure the invariance of certain de Branges spaces when certain composition operators, or adjoints of composition operators act on them. Most of these conditions are necessary and sufficient. Many examples are also included.
The last chapter contains a few miscellaneous results about range inclusions.
Poplicher, Mihaela Anca, "On some range inclusions" (1997). Doctoral Dissertations. 1979.