Heredity in fundamental left complemented algebras
In the present paper, we introduce the notion of a fundamental complemented linear space, through continuous projections. This notion is hereditary. Relative to this, we prove that if a certain topological algebra is fundamental, then a concrete subspace is fundamental too. For a fundamental complem...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2016-06-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v11/p11_06.pdf |
| _version_ | 1828454252443336704 |
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| author | Marina Haralampidou Konstantinos Tzironis |
| author_facet | Marina Haralampidou Konstantinos Tzironis |
| author_sort | Marina Haralampidou |
| collection | DOAJ |
| description | In the present paper, we introduce the notion of a fundamental complemented linear space, through continuous projections. This notion is hereditary. Relative to this, we prove that if a certain topological algebra is fundamental, then a concrete subspace is fundamental too. For a fundamental complemented linear space, we define the notion of continuity of the complementor. In some cases, we employ a generalized notion of complementation, that of (left) precomplementation. In our main result, the continuity of the complementor for a certain fundamental complemented (topological) algebra is inherited to the induced vector complementor of the underlying linear space of a certain right ideal. Weakly fundamental algebras are also considered in the context of locally convex ones. |
| first_indexed | 2024-12-11T00:19:14Z |
| format | Article |
| id | doaj.art-eb1d1b688e45475b82148ddb98169ae8 |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-12-11T00:19:14Z |
| publishDate | 2016-06-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-eb1d1b688e45475b82148ddb98169ae82022-12-22T01:27:50ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982016-06-0111 (2016)93106Heredity in fundamental left complemented algebrasMarina Haralampidou0Konstantinos Tzironis1Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece.Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece.In the present paper, we introduce the notion of a fundamental complemented linear space, through continuous projections. This notion is hereditary. Relative to this, we prove that if a certain topological algebra is fundamental, then a concrete subspace is fundamental too. For a fundamental complemented linear space, we define the notion of continuity of the complementor. In some cases, we employ a generalized notion of complementation, that of (left) precomplementation. In our main result, the continuity of the complementor for a certain fundamental complemented (topological) algebra is inherited to the induced vector complementor of the underlying linear space of a certain right ideal. Weakly fundamental algebras are also considered in the context of locally convex ones.http://www.utgjiu.ro/math/sma/v11/p11_06.pdfFundamental complemented algebracomplemented linear spacefundamental complemented (topological) linear spacevector complementorweakly fundamental algebraaxially closed element |
| spellingShingle | Marina Haralampidou Konstantinos Tzironis Heredity in fundamental left complemented algebras Surveys in Mathematics and its Applications Fundamental complemented algebra complemented linear space fundamental complemented (topological) linear space vector complementor weakly fundamental algebra axially closed element |
| title | Heredity in fundamental left complemented algebras |
| title_full | Heredity in fundamental left complemented algebras |
| title_fullStr | Heredity in fundamental left complemented algebras |
| title_full_unstemmed | Heredity in fundamental left complemented algebras |
| title_short | Heredity in fundamental left complemented algebras |
| title_sort | heredity in fundamental left complemented algebras |
| topic | Fundamental complemented algebra complemented linear space fundamental complemented (topological) linear space vector complementor weakly fundamental algebra axially closed element |
| url | http://www.utgjiu.ro/math/sma/v11/p11_06.pdf |
| work_keys_str_mv | AT marinaharalampidou heredityinfundamentalleftcomplementedalgebras AT konstantinostzironis heredityinfundamentalleftcomplementedalgebras |