Abstract
We describe sufficient conditions for the operator Lu = 1 g(x) L0u, with L0 an ordi- nary differential operator dissipative on its domain and a function g changing its sign, to have maximal semidefinite invariant subspaces in the Krein space L2,g(a,b) with the indefinite inner product (u,v )= b a g(x)u(x)v(x)dx. The semigroup properties of the restrictions of an operator to these subspaces are studied. The similarity problem of L to a selfadjoint operator is discussed.
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