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Über Positive Resolventenwerte Positiver Operatoren

Über Positive Resolventenwerte Positiver Operatoren 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 x∈A is a resolvent value of a positive element y∈A if and only if the element x satisfies the negative principle: If a∈A, λ < 0 and xa≤λa then xa≤ 0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Über Positive Resolventenwerte Positiver Operatoren

Scheffold, E.
Positivity , Volume 8 (2) – Oct 19, 2004
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1023/B:POST.0000042834.68084.16
Publisher site
See Article on Publisher Site

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 x∈A is a resolvent value of a positive element y∈A if and only if the element x satisfies the negative principle: If a∈A, λ < 0 and xa≤λa then xa≤ 0.

Journal

Positivity – Springer Journals

Published: Oct 19, 2004

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