Strictly Convex Banach Algebras
We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open questio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/221 |
| _version_ | 1797520225019625472 |
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| author | David Yost |
| author_facet | David Yost |
| author_sort | David Yost |
| collection | DOAJ |
| description | We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∗</mo></msup></semantics></math></inline-formula>-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there. |
| first_indexed | 2024-03-10T07:53:46Z |
| format | Article |
| id | doaj.art-fbbd064b0b2d43c582665537ec065aeb |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:53:46Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-fbbd064b0b2d43c582665537ec065aeb2023-11-22T12:03:12ZengMDPI AGAxioms2075-16802021-09-0110322110.3390/axioms10030221Strictly Convex Banach AlgebrasDavid Yost0Centre for Informatics and Applied Optimisation, Federation University, P.O. Box 663, Ballarat, VIC 3353, AustraliaWe discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∗</mo></msup></semantics></math></inline-formula>-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there.https://www.mdpi.com/2075-1680/10/3/221Banach spaceBanach algebrasmoothstrictly convex |
| spellingShingle | David Yost Strictly Convex Banach Algebras Axioms Banach space Banach algebra smooth strictly convex |
| title | Strictly Convex Banach Algebras |
| title_full | Strictly Convex Banach Algebras |
| title_fullStr | Strictly Convex Banach Algebras |
| title_full_unstemmed | Strictly Convex Banach Algebras |
| title_short | Strictly Convex Banach Algebras |
| title_sort | strictly convex banach algebras |
| topic | Banach space Banach algebra smooth strictly convex |
| url | https://www.mdpi.com/2075-1680/10/3/221 |
| work_keys_str_mv | AT davidyost strictlyconvexbanachalgebras |