Author:
Péter Berkics University of Pécs, Ifjúság útja 6, H-7624 Pécs, Hungary

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A linear operator on a Hilbert space , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if k+l:k,lGSGS*=.

In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.

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    Kato, T. Trotter’s product formula for an arbitrary pair of self-adjoint contraction semigroups. In Topics in Functional Analysis, vol. 3 of Advances in Mathematics Supplementary Studies. 1978, pp. 185195.

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    Kato, T. Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, 1980.

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    Sandovici, A. Von neumann’s theorem for linear relations. Linear and Multilinear Algebra (2017). doi:.

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    Sebestyén, Z., and Tarcsay, Z. Characterization of self-adjoint operators. Studia Scientiarum Mathematicarum Hungarica 50, 4 (2013), 423435. doi:.

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    Sebestyén, Z., and Tarcsay, Z. A reversed von neumann theorem. Acta Scientiarum Mathematicarum (Szeged) 80, 3–4 (2014), 659664.

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    Stone, M. Linear transformations in Hilbert space, vol. 15 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, Rhode Island, 1932.

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    von Neumann, J. Über adjungierte funktionaloperatoren. The Annals of Mathematics 33, 2 (1932). 294. Crossref. Web.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz, Linz, Austria)
  • Ferenc HARTUNG (University of Pannonia, Veszprém, Hungary)
  • Ferenc WEISZ (Eötvös Loránd University, Budapest, Hungary)

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Lukas SPIEGELHOFER (Montanuniversität Leoben, Leoben, Austria)
  • Andrea ŠVOB (University of Rijeka, Rijeka, Croatia)
  • Csaba SZÁNTÓ (Babeş-Bolyai University, Cluj-Napoca, Romania)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
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Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)