On a spectral decomposition of a commutative family of operators on spaces with indefinite metric. (English) Zbl 1100.47033
The authors prove existence of a joint spectral decomposition for a commutative family of operators on a Pontryagin or Krein space under the assumption that the operators have a common maximal non-negative invariant subspace represented as a direct sum of finite-dimensional neutral and uniformly positive subspaces. In contrast to the classical situation, a family possessing a joint spectral decomposition need not be generated by a single operator.
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:
47B50 | Linear operators on spaces with an indefinite metric |
46C20 | Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) |