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1997 | 66 | 1 | 155-172
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Selfadjoint operator matrices with finite rows

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EN
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EN
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.
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autor
  • Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland
autor
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
  • [1] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Part I, Comm. Pure Appl. Math. 14 (1961), 187-214.
  • [2] Yu. M. Berezanskiĭ, Eigenfunction Expansions for Selfadjoint Operators, Naukova Dumka, Kiev, 1965 (in Russian).
  • [3] T. Carleman, Sur la théorie mathématique de l'équation de Schrödinger, Ark. Mat. Astr. Fys. 24 (1934), 1-7.
  • [4] W. Dahmen and C. A. Micchelli, Banded matrices with banded inverses, II: locally finite decomposition of spline spaces, Constr. Approx 9 (1993), 263-281.
  • [5] S. Demko, Inverses of band matrices and local convergence of spline projectors, SIAM J. Numer. Anal. 14 (1977), 616-619.
  • [6] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, N.J., 1967.
  • [7] J. Janas, Unbounded Toeplitz operators in the Bargmann-Segal space, Studia Math. 99 (1991), 87-99.
  • [8] J. Janas and J. Stochel, Unbounded Toeplitz operators in the Segal-Bargmann space. II, J. Funct. Anal. 126 (1994), 418-447.
  • [9] P. E. T. Jørgensen, Approximately reducing subspaces for unbounded linear operators, J. Funct. Anal. 23 (1976), 392-414.
  • [10] P. E. T. Jørgensen, Essential self-adjointness of semibounded operators, Math. Ann. 237 (1978), 187-192.
  • [11] W. Mlak, The Schrödinger type couples related to weighted shifts, Univ. Iagel. Acta Math. 27 (1988), 297-301.
  • [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.
  • [14] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, New York, 1980.
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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv66z1p155bwm
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