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On norms in indefinite product spaces

Langer, M. and Luger, A. (2010) On norms in indefinite product spaces. In: Recent Advances in Operator Theory in Hilbert and Krein Spaces. Operator Theory: Advances and Applications, 198 . Birkhäuser, pp. 259-264. ISBN 978-3-0346-0179-5

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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.