M. Langer and A. Luger,
On norms in indefinite product spaces,
Oper. Theory Adv. Appl. 198 (2010), 259–264

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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