On the positive function of bounded type in Hilbert space. (English) Zbl 1164.47015
Summary: An invariant subspace theory for contractive transformations in Hilbert space as according to de Branges and Rovnyak is considered. We are interested in using reproducing kernel space methods in Hilbert space for the realization problem for functions of bounded type in the unit disk. The relation between factorization and invariant subspaces for continuous and contractive transformations in Hilbert space is discussed.
MSC:
47A48 | Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. |
47B34 | Kernel operators |
47A15 | Invariant subspaces of linear operators |
46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
30D50 | Blaschke products, etc. (MSC2000) |
47B50 | Linear operators on spaces with an indefinite metric |