Functorial properties of the lattice of functional semi-norms
Given a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi-norms. We further determine when this mappings preserves norms and observe that it does preserve certain other important properties. We next es...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000029 |
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| _version_ | 1832545672558018560 |
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| author | I. E. Schochetman S. K. Tsui |
| author_facet | I. E. Schochetman S. K. Tsui |
| author_sort | I. E. Schochetman |
| collection | DOAJ |
| description | Given a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi-norms. We further determine when this mappings preserves norms and observe that it does preserve certain other important properties. We next establish a functorial connection between measure spaces and lattice. Finally, we show that the above lattice mapping does not commute with the associate construction. |
| format | Article |
| id | doaj-art-c952e1365c3e4d11a072cf50f66d7542 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c952e1365c3e4d11a072cf50f66d75422025-02-03T07:25:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-0191172210.1155/S0161171286000029Functorial properties of the lattice of functional semi-normsI. E. Schochetman0S. K. Tsui1Oakland University, Rochester 48063, Michigan, USAOakland University, Rochester 48063, Michigan, USAGiven a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi-norms. We further determine when this mappings preserves norms and observe that it does preserve certain other important properties. We next establish a functorial connection between measure spaces and lattice. Finally, we show that the above lattice mapping does not commute with the associate construction.http://dx.doi.org/10.1155/S0161171286000029function semi-normassociate semi-normlattice of semi-normsmeasure-preserving transformationsemi-norm preservingassociate preservinglattice subhomomorphismcategoryfunctor. |
| spellingShingle | I. E. Schochetman S. K. Tsui Functorial properties of the lattice of functional semi-norms International Journal of Mathematics and Mathematical Sciences function semi-norm associate semi-norm lattice of semi-norms measure-preserving transformation semi-norm preserving associate preserving lattice subhomomorphism category functor. |
| title | Functorial properties of the lattice of functional semi-norms |
| title_full | Functorial properties of the lattice of functional semi-norms |
| title_fullStr | Functorial properties of the lattice of functional semi-norms |
| title_full_unstemmed | Functorial properties of the lattice of functional semi-norms |
| title_short | Functorial properties of the lattice of functional semi-norms |
| title_sort | functorial properties of the lattice of functional semi norms |
| topic | function semi-norm associate semi-norm lattice of semi-norms measure-preserving transformation semi-norm preserving associate preserving lattice subhomomorphism category functor. |
| url | http://dx.doi.org/10.1155/S0161171286000029 |
| work_keys_str_mv | AT ieschochetman functorialpropertiesofthelatticeoffunctionalseminorms AT sktsui functorialpropertiesofthelatticeoffunctionalseminorms |