# Selfadjoint operator matrices with finite rows

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 155-172
- ISSN: 0066-2216

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topJan Janas, and Jan Stochel. "Selfadjoint operator matrices with finite rows." Annales Polonici Mathematici 66.1 (1997): 155-172. <http://eudml.org/doc/269958>.

@article{JanJanas1997,

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.},

author = {Jan Janas, Jan Stochel},

journal = {Annales Polonici Mathematici},

keywords = {selfadjoint operator; band matrix; weighted shift; selfadjointness of symmetric operators with almost invariant subspaces; Carleman criterion; selfadjointness of Jacobi matrices; symmetric matrices with finite rows; Jørgensen’s criterion; hyponormal weighted shifts},

language = {eng},

number = {1},

pages = {155-172},

title = {Selfadjoint operator matrices with finite rows},

url = {http://eudml.org/doc/269958},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Jan Janas

AU - Jan Stochel

TI - Selfadjoint operator matrices with finite rows

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 155

EP - 172

AB - 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.

LA - eng

KW - selfadjoint operator; band matrix; weighted shift; selfadjointness of symmetric operators with almost invariant subspaces; Carleman criterion; selfadjointness of Jacobi matrices; symmetric matrices with finite rows; Jørgensen’s criterion; hyponormal weighted shifts

UR - http://eudml.org/doc/269958

ER -

## References

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- [8] J. Janas and J. Stochel, Unbounded Toeplitz operators in the Segal-Bargmann space. II, J. Funct. Anal. 126 (1994), 418-447. Zbl0824.47021
- [9] P. E. T. Jørgensen, Approximately reducing subspaces for unbounded linear operators, J. Funct. Anal. 23 (1976), 392-414. Zbl0341.47024
- [10] P. E. T. Jørgensen, Essential self-adjointness of semibounded operators, Math. Ann. 237 (1978), 187-192. Zbl0386.47010
- [11] W. Mlak, The Schrödinger type couples related to weighted shifts, Univ. Iagel. Acta Math. 27 (1988), 297-301. Zbl0695.47022
- [12] M. H. Stone, Linear Transformations in Hilbert Space and Their Applications to Analysis, Amer. Math. Soc. Colloq. Publ. 15, Amer. Math. Soc., Providence, R.I., 1932.
- [13] O. Toeplitz, Zur Theorie der quadratischen Formen von unendlichvielen Veränderlichen, Göttingen Nachr. 1910, 489-506. Zbl41.0381.02
- [14] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, New York, 1980. Zbl0434.47001

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