Duality for unbounded order convergence and applications
Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and Banach lattices. This paper presents a duality theory for unbounded order convergence. We define the unbounded order dual (or uo-dual) X u o ∼...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2018-07, Vol.22 (3), p.711-725 |
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| container_title | Positivity : an international journal devoted to the theory and applications of positivity in analysis |
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| creator | Gao, Niushan Leung, Denny H. Xanthos, Foivos |
| description | Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and Banach lattices. This paper presents a duality theory for unbounded order convergence. We define the unbounded order dual (or uo-dual)
X
u
o
∼
of a Banach lattice
X
and identify it as the order continuous part of the order continuous dual
X
n
∼
. The result allows us to characterize the Banach lattices that have order continuous preduals and to show that an order continuous predual is unique when it exists. Applications to the Fenchel–Moreau duality theory of convex functionals are given. The applications are of interest in the theory of risk measures in Mathematical Finance. |
| doi_str_mv | 10.1007/s11117-017-0539-0 |
| format | Article |
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X
u
o
∼
of a Banach lattice
X
and identify it as the order continuous part of the order continuous dual
X
n
∼
. The result allows us to characterize the Banach lattices that have order continuous preduals and to show that an order continuous predual is unique when it exists. Applications to the Fenchel–Moreau duality theory of convex functionals are given. The applications are of interest in the theory of risk measures in Mathematical Finance.</description><identifier>ISSN: 1385-1292</identifier><identifier>EISSN: 1572-9281</identifier><identifier>DOI: 10.1007/s11117-017-0539-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Calculus of Variations and Optimal Control; Optimization ; Convergence ; Econometrics ; Fourier Analysis ; Functionals ; Lattices (mathematics) ; Mathematics ; Mathematics and Statistics ; Operator Theory ; Potential Theory</subject><ispartof>Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2018-07, Vol.22 (3), p.711-725</ispartof><rights>Springer International Publishing AG 2017</rights><rights>Positivity is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-333c5eab06c0a0ee9fea13c04368d26c3f834516f2df52bef780b4d0ca21dc903</citedby><cites>FETCH-LOGICAL-c359t-333c5eab06c0a0ee9fea13c04368d26c3f834516f2df52bef780b4d0ca21dc903</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11117-017-0539-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11117-017-0539-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gao, Niushan</creatorcontrib><creatorcontrib>Leung, Denny H.</creatorcontrib><creatorcontrib>Xanthos, Foivos</creatorcontrib><title>Duality for unbounded order convergence and applications</title><title>Positivity : an international journal devoted to the theory and applications of positivity in analysis</title><addtitle>Positivity</addtitle><description>Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and Banach lattices. This paper presents a duality theory for unbounded order convergence. We define the unbounded order dual (or uo-dual)
X
u
o
∼
of a Banach lattice
X
and identify it as the order continuous part of the order continuous dual
X
n
∼
. The result allows us to characterize the Banach lattices that have order continuous preduals and to show that an order continuous predual is unique when it exists. Applications to the Fenchel–Moreau duality theory of convex functionals are given. 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X
u
o
∼
of a Banach lattice
X
and identify it as the order continuous part of the order continuous dual
X
n
∼
. The result allows us to characterize the Banach lattices that have order continuous preduals and to show that an order continuous predual is unique when it exists. Applications to the Fenchel–Moreau duality theory of convex functionals are given. The applications are of interest in the theory of risk measures in Mathematical Finance.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11117-017-0539-0</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2018-07, Vol.22 (3), p.711-725 |
| issn | 1385-1292 1572-9281 |
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| subjects | Calculus of Variations and Optimal Control Optimization Convergence Econometrics Fourier Analysis Functionals Lattices (mathematics) Mathematics Mathematics and Statistics Operator Theory Potential Theory |
| title | Duality for unbounded order convergence and applications |
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