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  • 1 Department of Sciences, University “Al. I. Cuza”, Lascăr Catargi 54, 700107 Iaşi, Romania
  • | 2 Department of Mathematics, University of Lille 1, 59655, Villeneuve d’Ascq, Cedex, France
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Abstract

A nonnegative linear relation S in a Hilbert space ℌ is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. A related quotient of the range of S is then provided with a natural inner product and the operators B and C induce two operators on the completion space. This construction is used to show the existence of self-adjoint and nonnegative extensions of the linear relations BS and CS, respectively.

  • [1] Arlinskiî, Yu. M., Hassi, S., Sebestyén, Z., Snoo de, H. S. V. 2001 On the class of extremal extensions of a nonnegative operator Oper. Theory: Adv. Appl. 127 4181 B. Sz.-Nagy memorial volume.

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    • Export Citation
  • [2] Aubin, J. P., Cellina, A. 1984 Differential Inclusions Springer-Verlag.

  • [3] Bernau, S. J. 1974 Products of positive operators Proc. Camb. Phil. Soc. 76 415416 .

  • [4] Dieudonne, J. A. 1961 Quasi-hermitian operators Proc. Inter. Symp. Linear Algebra Jerusalem Academic Press Jerusalem 115122 Israel, 1960.

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    • Export Citation
  • [5] Favini, A., Yagi, A. 1999 Degenerate Differential Equations in Banach Spaces Marcel Dekker New York–Basel–Hong Kong.

  • [6] Hassi, S., Sebestyén, Z., Snoo de, H. S. V. 2005 On the nonnegativity of operator products Acta Math. Hungar. 109 114 .

  • [7] Hassi, S., Sandovici, A., Snoo de, H. S. V., Winkler, H. 2007 A general factorization approach to the extension theory of nonnegative operators and relations J. Operator Theory 58 351368.

    • Search Google Scholar
    • Export Citation
  • [8] Prokaj, V., Sebestyén, Z. 1996 On Friedrichs extensions of operators Acta Sci. Math. (Szeged) 62 243246.

  • [9] Riesz, F., Sz.-Nagy, B. 1972 Lecons d’analyse fonctionnelle Akadémiai Kiadó Budapest.

  • [10] Sebestyén, Z. 2000 Positivity of operator products Acta Sci. Math. (Szeged) 66 287294.

  • [11] Sebestyén, Z., Stochel, J. 1991 Restrictions of positive self-adjoint operators Acta Sci. Math. (Szeged) 55 149154.

  • [12] Sebestyén, Z., Stochel, J. 2003 On products of unbounded operators Acta Math. Hungar. 100 105129 .

  • [13] Wigner, E. P. 1963 On weakly positive matrices Canad. J. Math. 15 313317 .

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
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Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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