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.
@article{bwmeta1.element.bwnjournal-article-apmv66z1p155bwm,
author = {Jan Janas and Jan Stochel},
title = {Selfadjoint operator matrices with finite rows},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {155-172},
zbl = {0894.47022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p155bwm}
}
Jan Janas; Jan Stochel. Selfadjoint operator matrices with finite rows. Annales Polonici Mathematici, Tome 66 (1997) pp. 155-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p155bwm/
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