Measures under the flat norm as ordered normed vector space

作者：Gwiazda Piotr; Marciniak Czochra Anna; Thieme Horst R^*

来源：Positivity, 2018, 22(1): 105-138.

DOI：10.1007/s11117-017-0503-z

• Measures
• Ordered normed vector space
• Homogeneous maps
• Spectral radius
• Krein-Rutman theorem
• Dynamical systems

The space of real Borel measures on a metric space S under the flat norm (dual bounded Lipschitz norm), ordered by the cone of nonnegative measures, is considered from an ordered normed vector space perspective in order to apply the well-developed theory of this area. The flat norm is considered in place of the variation norm because subsets of are compact and semiflows on are continuous under much weaker conditions. In turn, the flat norm offers new challenges because is rarely complete and is only complete if S is complete. As illustrations serve the eigenvalue problem for bounded additive and order-preserving homogeneous maps on and continuous semiflows. Both topics prepare for a dynamical systems theory on .

• 出版日期2018-3