Commuting compact self-adjoint operators on a pontryagin space

Bhattacharyya, Tirthankar ; Kosir, Tomaz (2001) Commuting compact self-adjoint operators on a pontryagin space Integral Equations and Operator Theory, 39 (4). pp. 377-386. ISSN 0378-620X

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Official URL: http://link.springer.com/article/10.1007/BF0120331...

Related URL: http://dx.doi.org/10.1007/BF01203319

Abstract

Suppose that A1,A2, ..., An are compact commuting self-adjoint linear maps on a Pontryagin space K of index k and that their joint root subspace M0 at the zero eigenvalue in ℂn is a nondegenerate subspace. Then there exist joint invariant subspaces H and F in K such that K=F⊗H,H is a Hilbert space and F is finite-dimensional space with k≤dimF≤(n+2)k. We also consider the structure of restrictions Aj|F in the case k=1.

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