The invariant subspace problem for absolutely p-summing operators in Krein spaces

Gerald Wanjala

doi:10.1186/1029-242x-2012-254

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

Introduction

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.

Results

Conclusion