Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Reflection symmetry and symmetrizability of Hilbert space operators


Authors: Zoltán Sebestyén and Jan Stochel
Journal: Proc. Amer. Math. Soc. 133 (2005), 1727-1731
MSC (2000): Primary 47A05, 47A10; Secondary 47B32
Published electronically: November 19, 2004
MathSciNet review: 2120258
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general factorization theorem for symmetrizable operators relating their spectra to spectra of selfadjoint operators induced by minimal factorizations is established. Its modified version essentially improves and completes a theorem of Jorgensen, which concerns diagonalizing operators with reflection symmetry.


References [Enhancements On Off] (What's this?)

  • 1. T. Ando, De Branges spaces and analytic operator functions, Lecture Note, Hokkaido University, Sapporo, Japan, 1990.
  • 2. E. Garbe, Zur Theorie der Integralgleichung dritter Art, Math. Annalen 76 (1915), 409-416.
  • 3. Palle E. T. Jorgensen, Diagonalizing operators with reflection symmetry, J. Funct. Anal. 190 (2002), no. 1, 93–132. Special issue dedicated to the memory of I. E. Segal. MR 1895530, 10.1006/jfan.2001.3881
  • 4. J. Marty, Valeurs singulières d'une équation de Fredholm, C.R. Acad. Sci., Paris 150 (1910), 1499-1502.
  • 5. A. J. Pell, Applications of biorthogonal systems of functions to the theory of integral equations, Trans. Amer. Math. Soc. 12 (1911), 165-180.
  • 6. Zoltán Sebestyén, Positivity of operator products, Acta Sci. Math. (Szeged) 66 (2000), no. 1-2, 287–294. MR 1768867
  • 7. Z. Sebestyén and J. Stochel, On products of unbounded operators, Acta Math. Hungar. 100 (2003), no. 1-2, 105–129. MR 1984863, 10.1023/A:1024660318703
  • 8. Irving Segal, Real spinor fields and the electroweak interaction, J. Funct. Anal. 154 (1998), no. 2, 542–558. MR 1612662, 10.1006/jfan.1997.3213
  • 9. Adriaan Cornelis Zaanen, Linear analysis. Measure and integral, Banach and Hilbert space, linear integral equations, Interscience Publishers Inc., New York; North-Holland Publishing Co., Amsterdam; P. Noordhoff N.V., Groningen, 1953. MR 0061752

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A05, 47A10, 47B32

Retrieve articles in all journals with MSC (2000): 47A05, 47A10, 47B32


Additional Information

Zoltán Sebestyén
Affiliation: Department of Applied Analysis, Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/c, Hungary
Email: sebesty@cs.elte.hu

Jan Stochel
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland
Email: stochel@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07705-6
Keywords: Operators in Hilbert space, de Branges space, factorizations of operator products, symmetrizable operators, operators with reflection symmetry
Received by editor(s): January 22, 2004
Received by editor(s) in revised form: February 14, 2004
Published electronically: November 19, 2004
Additional Notes: The research of the second author was supported by KBN grant 2 P03A 037 024
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society