Selfadjoint operator matrices with finite rows
Volume 66 / 1997
Annales Polonici Mathematici 66 (1997), 155-172
DOI: 10.4064/ap-66-1-155-172
Abstract
A generalization of the Carleman criterion for selfadjointness of Jacobi matrices to the case of symmetric matrices with finite rows is established. In particular, a new proof of the Carleman criterion is found. An extension of Jørgensen's criterion for selfadjointness of symmetric operators with "almost invariant" subspaces is obtained. Some applications to hyponormal weighted shifts are given.
