Examples of Positive Operators in Krein Space with 0 a Regular Critical Point of Innnite Rank
نویسندگان
چکیده
It is shown that the operators associated with the perturbed wave equation in IR n and with the elliptic operators with an indeenite weight function and mildly varying coeecients on IR n are similar to a selfadjoint operator in a Hilbert space. These operators have the whole IR as the spectrum. It is shown that they are positive operators in corresponding Krein spaces, and the whole problem is reduced to showing that 0 is not a singular critical point.
منابع مشابه
On Singular Critical Points of Positive Operators in Krein Spaces
We give an example of a positive operator B in a Krein space with the following properties: the nonzero spectrum of B consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of B are uniformly bounded and the point ∞ is a singular critical point of B. An operator A in the Krein space (K, [ · , · ]) is said to be positive ...
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