Isometries of a function space
It is proved here that an isometry on the subset of all positive functions of L1⋂Lp(ℝ) can be characterized by means of a function h together with a Borel measurable mapping ϕ of ℝ, thus generalizing the Banach-Lamparti theorem of Lp spaces.
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000735 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553748575027200 |
|---|---|
| author | U. D. Vyas |
| author_facet | U. D. Vyas |
| author_sort | U. D. Vyas |
| collection | DOAJ |
| description | It is proved here that an isometry on the subset of all positive functions of L1⋂Lp(ℝ) can be characterized by means of a function h together with a Borel measurable mapping ϕ of ℝ, thus generalizing the Banach-Lamparti theorem of Lp spaces. |
| format | Article |
| id | doaj-art-635b196de94c41b0b5446bb07892dc75 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-635b196de94c41b0b5446bb07892dc752025-02-03T05:53:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110361561910.1155/S0161171287000735Isometries of a function spaceU. D. Vyas0Department of Mathematics and Computer Science, Winston-Salem State University, Winston-Salem, North Carolina 27110, USAIt is proved here that an isometry on the subset of all positive functions of L1⋂Lp(ℝ) can be characterized by means of a function h together with a Borel measurable mapping ϕ of ℝ, thus generalizing the Banach-Lamparti theorem of Lp spaces.http://dx.doi.org/10.1155/S0161171287000735Borel measurefunction spaceBanach-Lamparti theorem. |
| spellingShingle | U. D. Vyas Isometries of a function space International Journal of Mathematics and Mathematical Sciences Borel measure function space Banach-Lamparti theorem. |
| title | Isometries of a function space |
| title_full | Isometries of a function space |
| title_fullStr | Isometries of a function space |
| title_full_unstemmed | Isometries of a function space |
| title_short | Isometries of a function space |
| title_sort | isometries of a function space |
| topic | Borel measure function space Banach-Lamparti theorem. |
| url | http://dx.doi.org/10.1155/S0161171287000735 |
| work_keys_str_mv | AT udvyas isometriesofafunctionspace |