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On commuting compact self-adjoint operators on a Pontryagin space

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Abstract

Suppose thatA 1,A 2, ...,A n are compact commuting self-adjoint linear maps on a Pontryagin spaceK of indexk and that their joint root subspaceM 0 at the zero eigenvalue in ℂn is a nondegenerate subspace. Then there exist joint invariant subspacesH andF inK such thatK=F⊗H,H is a Hilbert space andF is finite-dimensional space withk≤dimF≤(n+2)k. We also consider the structure of restrictionsA j|F in the casek=1.

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Author notes

  1. Tirthankar Bhattacharyya

    Present address: Department of Mathematics, Indian Institute of Science, 560012, Bangalore, India

Authors and Affiliations

  1. Poorna Prajna Institute for Scientific Research, 4 Sadshivnagar, 560080, Bangalore, India

    Tirthankar Bhattacharyya

  2. Department of Mathematics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Tomaž Koŝir

Authors
  1. Tirthankar Bhattacharyya
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  2. Tomaž Koŝir
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Bhattacharyya, T., Koŝir, T. On commuting compact self-adjoint operators on a Pontryagin space. Integr equ oper theory 39, 377–386 (2001). https://doi.org/10.1007/BF01203319

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  • DOI: https://doi.org/10.1007/BF01203319

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