Measures under the flat norm as ordered normed vector space
The space of real Borel measures M(S)M(S)\mathcal {M}(S) on a metric space S under the flat norm (dual bounded Lipschitz norm), ordered by the cone M+(S)M+(S)\mathcal {M}_+(S) of nonnegative measures, is considered from an ordered normed vector space perspective in order to apply the well-developed...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2018
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| In: |
Positivity
Year: 2017, Volume: 22, Issue: 1, Pages: 105-138 |
| ISSN: | 1572-9281 |
| DOI: | 10.1007/s11117-017-0503-z |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s11117-017-0503-z Verlag, Volltext: https://link.springer.com/article/10.1007/s11117-017-0503-z Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2Fs11117-017-0503-z.pdf 
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| Author Notes: | Piotr Gwiazda, Anna Marciniak-Czochra, Horst R. Thieme |
| Summary: | The space of real Borel measures M(S)M(S)\mathcal {M}(S) on a metric space S under the flat norm (dual bounded Lipschitz norm), ordered by the cone M+(S)M+(S)\mathcal {M}_+(S) 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 M+(S)M+(S)\mathcal {M}_+(S) are compact and semiflows on M+(S)M+(S)\mathcal {M}_+(S) are continuous under much weaker conditions. In turn, the flat norm offers new challenges because M(S)M(S)\mathcal {M}(S) is rarely complete and M+(S)M+(S)\mathcal {M}_+(S) is only complete if S is complete. As illustrations serve the eigenvalue problem for bounded additive and order-preserving homogeneous maps on M+(S)M+(S)\mathcal {M}_+(S) and continuous semiflows. Both topics prepare for a dynamical systems theory on M+(S)M+(S)\mathcal {M}_+(S). |
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| Item Description: | Gesehen am 28.06.2018 Published online: 25 May 2017 |
| Physical Description: | Online Resource |
| ISSN: | 1572-9281 |
| DOI: | 10.1007/s11117-017-0503-z |