Über Positive Resolventenwerte Positiver Operatoren


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Abstract

In this paper we study the positive resolvent values of positive operators respectively of positive elements in Banach lattice ordered algebras. In the matrix case these values are just the inverse M-matrices. One of the main results is the following: Let A be a Banach lattice ordered algebra. A positive invertible element xA is a resolvent value of a positive element yA if and only if the element x satisfies the negative principle: If aA, λ < 0 and xa ≤ λa then xa ≤ 0.

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