A formula to calculate the spectral radius of a compact linear operator
There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operator T defined o...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000793 |
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| _version_ | 1832561612654903296 |
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| author | Fernando Garibay Bonales Rigoberto Vera Mendoza |
| author_facet | Fernando Garibay Bonales Rigoberto Vera Mendoza |
| author_sort | Fernando Garibay Bonales |
| collection | DOAJ |
| description | There is a formula (Gelfand's formula) to find the spectral radius of a linear operator
defined on a Banach space. That formula does not apply even in normed spaces which are not complete.
In this paper we show a formula to find the spectral radius of any linear and compact operator T defined
on a complete topological vector space, locally convex. We also show an easy way to find a non-trivial
T-invariant closed subspace in terms of Minkowski functional. |
| format | Article |
| id | doaj-art-099d8626c1374b81aece47874392b5d9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-099d8626c1374b81aece47874392b5d92025-02-03T01:24:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120358558810.1155/S0161171297000793A formula to calculate the spectral radius of a compact linear operatorFernando Garibay Bonales0Rigoberto Vera Mendoza1Escuela de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio B. Ciudad Universitaria, Morelia, Michoacán 58060, MexicoEscuela de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio B. Ciudad Universitaria, Morelia, Michoacán 58060, MexicoThere is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operator T defined on a complete topological vector space, locally convex. We also show an easy way to find a non-trivial T-invariant closed subspace in terms of Minkowski functional.http://dx.doi.org/10.1155/S0161171297000793compact linear operatorspectral radiuslocally convex topological linear spaceinvariant subspacenetsultimately bounded nets. |
| spellingShingle | Fernando Garibay Bonales Rigoberto Vera Mendoza A formula to calculate the spectral radius of a compact linear operator International Journal of Mathematics and Mathematical Sciences compact linear operator spectral radius locally convex topological linear space invariant subspace nets ultimately bounded nets. |
| title | A formula to calculate the spectral radius of a compact linear operator |
| title_full | A formula to calculate the spectral radius of a compact linear operator |
| title_fullStr | A formula to calculate the spectral radius of a compact linear operator |
| title_full_unstemmed | A formula to calculate the spectral radius of a compact linear operator |
| title_short | A formula to calculate the spectral radius of a compact linear operator |
| title_sort | formula to calculate the spectral radius of a compact linear operator |
| topic | compact linear operator spectral radius locally convex topological linear space invariant subspace nets ultimately bounded nets. |
| url | http://dx.doi.org/10.1155/S0161171297000793 |
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