Abstract
Let A be a positive operator with a nonempty resolvent set in a Krein space K. Then A has a spectral function with 0 and ∞ being the only possible critical points, see [9]; if neither of these points is a singular critical point then A is similar to a Hilbert space selfadjoint operator, that is, it is a scalar operator with real spectrum (see [9] for the definition and properties of the Krein space operators).
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Branko Najman passed away before this manuscript was completed.
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Dedicated to Heinz Langer on the occasion of his 60th birthday
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Najman, B., Veselić, K. (1998). Multiplicative perturbations of positive operators in Krein spaces. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_18
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