The order of neutrality for linear operators on inner product spaces

P. Lancaster, A. S. Markus, P. Zizler

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let A be a symmetric linear operator defined on all of a (possibly degenerate) indefinite inner product space ℋ. Let script N sign be the set of all subspaces of ℋ which are A-invariant, neutral (in the sense of the indefinite scalar product), and finite dimensional. It is shown that members of script N sign which are maximal (with respect to inclusion) all have the same dimension. This is called the "order of neutrality" of A and admits immediate application to self-adjoint operators on a Pontrjagin space.

Original languageEnglish
Pages (from-to)25-29
Number of pages5
JournalLinear Algebra and Its Applications
Volume259
Issue number1-3
DOIs
StatePublished - 1 Jul 1997

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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