Linear mappings on ordered vector spaces

  • Tobias Damm
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 297)


Before we can start to analyze the generalized Riccati operators derived in the previous chapter, we have to deal with generalized Lyapunov operators of the type occuring e.g. in Theorem 1.5.3. It is crucial to observe that these Lyapunov operators possess certain positivity properties, which will be discussed in the following. The present chapter is split in two parts. In the first part, we introduce the general notions of ordered Banach spaces and resolvent positive operators, which is the set-up to be used in Chapter 4. In the second part, we focus on the ordered vector space \(\mathcal{H}^n\) of Hermitian matrices, which is relevant for our further investigations in Chapter 5.


Positive Operator Convex Cone Real Banach Space Hermitian Matrice Closed Convex Cone 
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Authors and Affiliations

  • Tobias Damm
    • 1
  1. 1.Technische Universität Braunschweig Institut für Angewandte Mathematik 38023 BraunschweigGermany

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