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On the boundedness of Hamiltonian operators


Authors: Tomas Ya. Azizov, Aad Dijksma and Irina V. Gridneva
Journal: Proc. Amer. Math. Soc. 131 (2003), 563-576
MSC (2000): Primary 47B50, 46C20, 47B44, 47B25
DOI: https://doi.org/10.1090/S0002-9939-02-06565-6
Published electronically: May 29, 2002
MathSciNet review: 1933348
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Abstract: We show that a non-negative Hamiltonian operator whose domain contains a maximal uniformly positive subspace is bounded.


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  • [AI] T.YA. AZIZOV AND I.S. IOKHVIDOV, Foundations of the theory of linear operators in spaces with an indefinite metric, Nauka, Moscow, 1986 (Russian); English transl.: Linear operators in spaces with an indefinite metric, Wiley, New York, 1989. MR 90j:47042
  • [AKK] T.YA. AZIZOV, V.K. KIRIAKIDI, AND G.A. KURINA, An indefinite approach to the reduction of a non-negative Hamiltonian operator function to a block diagonal form, Funct. Anal. and Appl., 35 (3), 2001, 73-75 (Russian).
  • [B] M.L. Brodskii, On the properties of an operator mapping into itself the non-negative part of a space with an indefinite metric, Uspekhi Mat. Naut 14 (1), 1959, 147-152 (Russian). MR 21:5145
  • [DR] M.A. DRITSCHEL, J. ROVNYAK, Extension theorems for contraction operators on Krein spaces, Operator Theory: Adv. Appl., vol. 47, Birkhäuser Verlag, Basel, 1990, 221-305. MR 92m:47068
  • [KL] M.G. KREIN AND H. LANGER, On some mathematical principles in the linear theory of damped oscillations of continua, Proc. Int. Sympos. on Applications of the Theory of Functions in Continuum Mechanics, Tbilisi, 1963, Vol. II: Fluid and Gas Mechanics, Math. Methods, Moscow, 1965, 283-322 (Russian); English transl.: Integral Equations Operator Theory 1, 1978, 364-399 and 539-566. MR 80d:47026; MR 80h:47022
  • [L1] H. LANGER, Zur Spektraltheorie $J$-selbstadjungierter Operatoren, Math. Ann. 146 (1), 1962, 60-85. MR 25:1450
  • [L2] H. LANGER, Eine Verallgemeinerung eines Satzes von L.S. Pontrjagin, Math. Ann. 152 (5), 1963, 434-436. MR 28:1492
  • [LT] H. LANGER AND CHR. TRETTER, Spectral decomposition of some nonselfadjoint block operator matrices, J. of Operator Theory 39, 1998, 339-359. MR 99d:47004
  • [S] A.A. SHKALIKOV, On the existence of invariant subspaces of dissipative operators in an inner product space, Fund. and Appl. Math. 5 (2), 1999, 627-635 (Russian). MR 2001k:47051
  • [Shm] YU.L. SHMUL'YAN, Division in the class of $J$-expansive operators, Mat. Sb. (N.S.) 74 (116), 1967, 516-525 (Russian); English transl.: Math. USSR-Sbornik 3, 1967, 471-479.

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Additional Information

Tomas Ya. Azizov
Affiliation: Department of Mathematics, Voronezh State University, 394693 Voronezh, Russia
Email: azizov@tom.vsu.ru

Aad Dijksma
Affiliation: Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, the Netherlands
Email: dijksma@math.rug.nl

Irina V. Gridneva
Affiliation: Department of Mathematics, Voronezh State University, 394693 Voronezh, Russia

DOI: https://doi.org/10.1090/S0002-9939-02-06565-6
Received by editor(s): March 13, 2001
Received by editor(s) in revised form: September 28, 2001
Published electronically: May 29, 2002
Additional Notes: This research was supported by grants NWO 047-008-008 and RFBR 99-01-00391
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society

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