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Reflection symmetry and symmetrizability of Hilbert space operators
Author(s):
Zoltán
Sebestyén;
Jan
Stochel
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1727-1731.
MSC (2000):
Primary 47A05, 47A10;
Secondary 47B32
Posted:
November 19, 2004
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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.
References:
- 1.
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- E. Garbe, Zur Theorie der Integralgleichung dritter Art, Math. Annalen 76 (1915), 409-416.
- 3.
- P. E. T. Jorgensen, Diagonalizing operators with reflection symmetry, J. Funct. Anal. 190 (2002), 93-132. MR 1895530 (2003e:47069)
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- Z. Sebestyén, J. Stochel, On products of unbounded operators, Acta Math. Hungar., 100 (2003), 105-129. MR 1984863 (2004c:47003)
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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 Jagiellonski, Reymonta 4, 30-059 Kraków, Poland
Email:
stochel@im.uj.edu.pl
DOI:
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
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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