g-Bases in Hilbert Spaces
The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/923729 |
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| _version_ | 1849395945393881088 |
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| author | Xunxiang Guo |
| author_facet | Xunxiang Guo |
| author_sort | Xunxiang Guo |
| collection | DOAJ |
| description | The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of g-bases and g-orthonormal bases. And the property of g-minimal of g-bases is studied as well. Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces. |
| format | Article |
| id | doaj-art-b5a78dd4e96b4df981b12d5cd18c5194 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b5a78dd4e96b4df981b12d5cd18c51942025-08-20T03:39:28ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/923729923729g-Bases in Hilbert SpacesXunxiang Guo0Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaThe concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of g-bases and g-orthonormal bases. And the property of g-minimal of g-bases is studied as well. Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces.http://dx.doi.org/10.1155/2012/923729 |
| spellingShingle | Xunxiang Guo g-Bases in Hilbert Spaces Abstract and Applied Analysis |
| title | g-Bases in Hilbert Spaces |
| title_full | g-Bases in Hilbert Spaces |
| title_fullStr | g-Bases in Hilbert Spaces |
| title_full_unstemmed | g-Bases in Hilbert Spaces |
| title_short | g-Bases in Hilbert Spaces |
| title_sort | g bases in hilbert spaces |
| url | http://dx.doi.org/10.1155/2012/923729 |
| work_keys_str_mv | AT xunxiangguo gbasesinhilbertspaces |