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Spectral Doubling of Normal Operators and Connections with Antiunitary Operators.
- Source :
- Integral Equations & Operator Theory; Jan2012, Vol. 72 Issue 1, p115-130, 16p
- Publication Year :
- 2012
-
Abstract
- Equations such as AB = B A have been studied in the finite dimensional setting in (Linear Algebra Appl 369:279-294, ). These equations have implications for the spectrum of B, when A is normal. Our aim is to generalize these results to an infinite dimensional setting. In this case it is natural to use JB* J for some conjugation operator J in place of B. Our main result is a spectral pairing theorem for a bounded normal operator B which is applied to the study of the equation KB = B* K for K an antiunitary operator. In particular, using conjugation operators, we generalize the notion of Hamiltonian operator and skew-Hamiltonian operator in a natural way, derive some of their properties, and give a characterization of certain operators B for which AB = ( JB* J) A and BA = A( JB* J) and also those B with KB = B* K for certain antiunitary operators K. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0378620X
- Volume :
- 72
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Integral Equations & Operator Theory
- Publication Type :
- Academic Journal
- Accession number :
- 70130544
- Full Text :
- https://doi.org/10.1007/s00020-011-1910-3