Geodesic
Norms with Infinite Values
Journal of convex analysis, Tome 22 (2015) no. 1, pp. 37-6
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We provide an overview of linear spaces equipped with norms that may take on the value infinity but that otherwise satisfy the properties of ordinary norms. Spaces equipped with such norms fail to be topological vector spaces unless the norm is finite valued. We study the continuous linear transformations between such spaces, extending the theory of conventional linear analysis in often unanticipated ways.
Classification : 46B20, 46B28, 46A17, 46E15, 26A16
Mots-clés : Extended norm, infinite valued norm, projection operator, projection complement, bornology, operator norm, effective domain, uniform convergence on bounded subsets, extended supremum norm, extended Lipschitz norm, distance basis 
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     author = {G. Beer},
     title = {Norms with {Infinite} {Values}},
     journal = {Journal of convex analysis},
     pages = {37--6},
     year = {2015},
     volume = {22},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a2/}
}
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G. Beer. Norms with Infinite Values. Journal of convex analysis, Tome 22 (2015) no. 1, pp. 37-6. http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a2/