A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces
Nirenberg proposed a problem as to whether or not a continuous and expansive operator T:X⟶X (where X is a Hilbert space) is surjective if RT∘≠∅. I shall give a positive answer for the problem provided that RT∘ is unbounded. For contents related to this paper, the reader is referred to the remarks an...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/9487405 |
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| _version_ | 1832552988597551104 |
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| author | Teffera M. Asfaw |
| author_facet | Teffera M. Asfaw |
| author_sort | Teffera M. Asfaw |
| collection | DOAJ |
| description | Nirenberg proposed a problem as to whether or not a continuous and expansive operator T:X⟶X (where X is a Hilbert space) is surjective if RT∘≠∅. I shall give a positive answer for the problem provided that RT∘ is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years. |
| format | Article |
| id | doaj-art-763f40168f0247c1be06e2bf0abcb52a |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-763f40168f0247c1be06e2bf0abcb52a2025-02-03T05:57:20ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/9487405A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert SpacesTeffera M. Asfaw0Department of MathematicsNirenberg proposed a problem as to whether or not a continuous and expansive operator T:X⟶X (where X is a Hilbert space) is surjective if RT∘≠∅. I shall give a positive answer for the problem provided that RT∘ is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years.http://dx.doi.org/10.1155/2022/9487405 |
| spellingShingle | Teffera M. Asfaw A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces Abstract and Applied Analysis |
| title | A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces |
| title_full | A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces |
| title_fullStr | A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces |
| title_full_unstemmed | A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces |
| title_short | A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces |
| title_sort | positive answer on nirenberg s problem on expansive mappings in hilbert spaces |
| url | http://dx.doi.org/10.1155/2022/9487405 |
| work_keys_str_mv | AT tefferamasfaw apositiveansweronnirenbergsproblemonexpansivemappingsinhilbertspaces AT tefferamasfaw positiveansweronnirenbergsproblemonexpansivemappingsinhilbertspaces |