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<p>We consider a self-adjoint operator acting in a Krein space and possessing an invariant subspace that is maximal nonnegative and is decomposed into a direct sum of a uniformly positive (i.e., equivalent to a Hilbert space with respect to the inner pseudoscalar product) and a finite-dimensional neutral subspace. We prove the existence of a difference expression that transforms the moment sequence generated by this operator into a sequence representable as a difference of positive moment sequences. In the case of a cyclic operator, we apply this result to construct a function space in which the operator under study is modelled as an operator of multiplication by an independent variable.</p>

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SPECTRAL DECOMPOSITIONS OF SELF-ADJOINT OPERATORS IN PONTRYAGIN AND KREIN SPACES

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • V. A. Strauss

摘要

We consider a self-adjoint operator acting in a Krein space and possessing an invariant subspace that is maximal nonnegative and is decomposed into a direct sum of a uniformly positive (i.e., equivalent to a Hilbert space with respect to the inner pseudoscalar product) and a finite-dimensional neutral subspace. We prove the existence of a difference expression that transforms the moment sequence generated by this operator into a sequence representable as a difference of positive moment sequences. In the case of a cyclic operator, we apply this result to construct a function space in which the operator under study is modelled as an operator of multiplication by an independent variable.