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Proceedings of the American Mathematical Society
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
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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.


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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
PII: S 0002-9939(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