On the surjectivity of linear transformations
Let B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given v∈X there is a solution for the equation Tu=v. This result is used to discuss the existence of an Lp-weak soluti...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296000750 |
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| _version_ | 1832558210453602304 |
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| author | M. Damlakhi V. Anandam |
| author_facet | M. Damlakhi V. Anandam |
| author_sort | M. Damlakhi |
| collection | DOAJ |
| description | Let B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given v∈X there is a solution for the equation Tu=v. This result is used to discuss the existence of an Lp-weak solution of Du=v where D is a differential operator with smooth coefficients and v∈Lp. |
| format | Article |
| id | doaj-art-e6bea7ffeacb4fda8ca90cffdf03c4d1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e6bea7ffeacb4fda8ca90cffdf03c4d12025-02-03T01:32:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119354554810.1155/S0161171296000750On the surjectivity of linear transformationsM. Damlakhi0V. Anandam1Department of Mathematics, King Saud University, P O Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, King Saud University, P O Box 2455, Riyadh 11451, Saudi ArabiaLet B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given v∈X there is a solution for the equation Tu=v. This result is used to discuss the existence of an Lp-weak solution of Du=v where D is a differential operator with smooth coefficients and v∈Lp.http://dx.doi.org/10.1155/S0161171296000750Admissible linear operatorsLp-functionsharmonic functions. |
| spellingShingle | M. Damlakhi V. Anandam On the surjectivity of linear transformations International Journal of Mathematics and Mathematical Sciences Admissible linear operators Lp-functions harmonic functions. |
| title | On the surjectivity of linear transformations |
| title_full | On the surjectivity of linear transformations |
| title_fullStr | On the surjectivity of linear transformations |
| title_full_unstemmed | On the surjectivity of linear transformations |
| title_short | On the surjectivity of linear transformations |
| title_sort | on the surjectivity of linear transformations |
| topic | Admissible linear operators Lp-functions harmonic functions. |
| url | http://dx.doi.org/10.1155/S0161171296000750 |
| work_keys_str_mv | AT mdamlakhi onthesurjectivityoflineartransformations AT vanandam onthesurjectivityoflineartransformations |