Abstract
In a Krein space various norms can be defined by choosing different underlying fundamental decompositions. In this note we consider this dependence explicitly and draw the conclusion that — even in a Pontryagin space — there does not exist a natural choice motivated by minimizing properties.
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References
J. Bognár, Indefinite inner product spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, 1974.
R. Nevanlinna, Erweiterung der Theorie des Hilbertschen Raumes, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] (1952), 160–168.
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In memory of Peter Jonas, who knew Krein spaces so well
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Langer, M., Luger, A. (2009). On Norms in Indefinite Inner Product Spaces. In: Behrndt, J., Förster, KH., Trunk, C. (eds) Recent Advances in Operator Theory in Hilbert and Krein Spaces. Operator Theory: Advances and Applications, vol 198. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0180-1_14
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DOI: https://doi.org/10.1007/978-3-0346-0180-1_14
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0179-5
Online ISBN: 978-3-0346-0180-1
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