Integral Equations and Operator Theory

, Volume 25, Issue 1, pp 58–72 | Cite as

Index formulae for subspaces of Kreîn spaces

  • AAD Dijksma
  • Aurelian Gheondea
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Abstract

For a subspaceS of a Kreîn spaceK and an arbitrary fundamental decompositionK=K−[+]K+ ofK, we prove the index formula
$$\kappa ^ - \left( \mathcal{S} \right) + \dim \left( {\mathcal{S}^ \bot \cap \mathcal{K}^ + } \right) = \kappa ^ + \left( {\mathcal{S}^ \bot } \right) + \dim \left( {\mathcal{S} \cap \mathcal{K}^ - } \right)$$
where κ±(S) stands for the positive/negative signature ofS. The difference dim(S∩K−)−dim(S⊥∩K+), provided it is well defined, is called the index ofS. The formula turns out to unify other known index formulac for operators or subspaces in a Kreîn space.

AMS Classification Numbers

46C20 47B50 47A53 
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Copyright information

© Birkhäuser-Verlag 1996

Authors and Affiliations

  • AAD Dijksma
    • 1
  • Aurelian Gheondea
    • 2
  1. 1.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Institutul de Matematicâ alAcademiei RomäneBucureştiRomânia

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