Abstract
Let 1≤p<∞, and let T be a bounded linear operator defined on a Krein space K. We prove the existence of a non-positive subspace L − of K invariant under T with the assumption that T is absolutely p-summing with some further conditions imposed on it.MSC:47B50, 46C20, 47B10.
Highlights
In this article we consider the question of the existence of a non-negative subspace invariant under an absolutely p-summing operator T defined on a Krein space K
We turn to the main problem under consideration here, which is the question of the existence of semi-definite invariant subspaces for absolutely p-summing operators on a Krein space K
It is the aim of this paper to prove the existence of a non-positive invariant subspace for an absolutely p-summing operator T acting on a Krein space K and having the following properties: (i) there exists a circle := {ξ ∈ C : |ξ | = r} which separates the spectrum of T for which the scalar multiple ξ R(ξ ) of the resolvent operator
Summary
In this article we consider the question of the existence of a non-negative subspace invariant under an absolutely p-summing operator T defined on a Krein space K. We turn to the main problem under consideration here, which is the question of the existence of semi-definite invariant subspaces for absolutely p-summing operators on a Krein space K.
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