The Cayley transform of Banach algebras
The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn=0) if and only if it is the Cayley transform CA=(I−A)−1(I+A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007962 |
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| _version_ | 1849400085649031168 |
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| author | Zhidong Pan |
| author_facet | Zhidong Pan |
| author_sort | Zhidong Pan |
| collection | DOAJ |
| description | The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn=0) if and only if it is the Cayley transform CA=(I−A)−1(I+A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras. |
| format | Article |
| id | doaj-art-a024fffdf1de40fe844b88dda8ca237a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a024fffdf1de40fe844b88dda8ca237a2025-08-20T03:38:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129742742810.1155/S0161171202007962The Cayley transform of Banach algebrasZhidong Pan0Department of Mathematics, Saginaw Valley State University, University Center 48710, MI, USAThe main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn=0) if and only if it is the Cayley transform CA=(I−A)−1(I+A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.http://dx.doi.org/10.1155/S0161171202007962 |
| spellingShingle | Zhidong Pan The Cayley transform of Banach algebras International Journal of Mathematics and Mathematical Sciences |
| title | The Cayley transform of Banach algebras |
| title_full | The Cayley transform of Banach algebras |
| title_fullStr | The Cayley transform of Banach algebras |
| title_full_unstemmed | The Cayley transform of Banach algebras |
| title_short | The Cayley transform of Banach algebras |
| title_sort | cayley transform of banach algebras |
| url | http://dx.doi.org/10.1155/S0161171202007962 |
| work_keys_str_mv | AT zhidongpan thecayleytransformofbanachalgebras AT zhidongpan cayleytransformofbanachalgebras |