On Supra-Additive and Supra-Multiplicative Maps
Let A and B be ordered algebras over ℝ, where A has a generating positive cone and B satisfies the property that b2>0 if 0≠b∈B. We give some conditions for a map T:A→B which is supra-additive and supra-multiplicative for all positive and negative elements to be linear and multiplicative; that is,...
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Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/108535 |
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doaj-79a52408f58e44848d83141c0ca1ae742020-11-25T00:59:19ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/108535108535On Supra-Additive and Supra-Multiplicative MapsJin Xi Chen0Zi Li Chen1College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaDepartment of Mathematics, Southwest Jiaotong University, Chengdu 610031, ChinaLet A and B be ordered algebras over ℝ, where A has a generating positive cone and B satisfies the property that b2>0 if 0≠b∈B. We give some conditions for a map T:A→B which is supra-additive and supra-multiplicative for all positive and negative elements to be linear and multiplicative; that is, T is a homomorphism of algebras. Our results generalize some known results on supra-additive and supra-multiplicative maps between spaces of real functions.http://dx.doi.org/10.1155/2013/108535 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jin Xi Chen Zi Li Chen |
| spellingShingle |
Jin Xi Chen Zi Li Chen On Supra-Additive and Supra-Multiplicative Maps Journal of Function Spaces and Applications |
| author_facet |
Jin Xi Chen Zi Li Chen |
| author_sort |
Jin Xi Chen |
| title |
On Supra-Additive and Supra-Multiplicative Maps |
| title_short |
On Supra-Additive and Supra-Multiplicative Maps |
| title_full |
On Supra-Additive and Supra-Multiplicative Maps |
| title_fullStr |
On Supra-Additive and Supra-Multiplicative Maps |
| title_full_unstemmed |
On Supra-Additive and Supra-Multiplicative Maps |
| title_sort |
on supra-additive and supra-multiplicative maps |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2013-01-01 |
| description |
Let A and B be ordered algebras over ℝ, where A has a generating positive cone and B satisfies the property that b2>0 if 0≠b∈B. We give some conditions for a map T:A→B which is supra-additive and supra-multiplicative for all positive and negative elements to be linear and multiplicative; that is, T is a homomorphism of algebras. Our results generalize some known results on supra-additive and supra-multiplicative maps between spaces of real functions. |
| url |
http://dx.doi.org/10.1155/2013/108535 |
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