Spectral integration and spectral theory for non-Archimedean Banach spaces
Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebra ℒ(E) of the conti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120201150X |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558385619271680 |
|---|---|
| author | S. Ludkovsky B. Diarra |
| author_facet | S. Ludkovsky B. Diarra |
| author_sort | S. Ludkovsky |
| collection | DOAJ |
| description | Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are
different types of Banach spaces over non-Archimedean
fields. We have determined the spectrum of some closed commutative
subalgebras of the Banach algebra ℒ(E) of the continuous linear operators on a free Banach space E generated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of
Stone theorem. It also contains the case of C-algebras C∞(X,𝕂). We prove a particular case of a representation of a C-algebra with the help of a L(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral
theorems for operators and families of commuting linear continuous
operators on the non-Archimedean Banach space. |
| format | Article |
| id | doaj-art-52c4ffb37af84b62b3da9e990f6f974b |
| 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-52c4ffb37af84b62b3da9e990f6f974b2025-02-03T01:32:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131742144210.1155/S016117120201150XSpectral integration and spectral theory for non-Archimedean Banach spacesS. Ludkovsky0B. Diarra1Theoretical Department, Institute of General Physics, 38, Vavilov Street, Moscow 119991, RussiaLaboratoire de Mathématiques Pures, Complexe Scientifique des Cézeaux, Aubière 63 177 , FranceBanach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebra ℒ(E) of the continuous linear operators on a free Banach space E generated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case of C-algebras C∞(X,𝕂). We prove a particular case of a representation of a C-algebra with the help of a L(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.http://dx.doi.org/10.1155/S016117120201150X |
| spellingShingle | S. Ludkovsky B. Diarra Spectral integration and spectral theory for non-Archimedean Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Spectral integration and spectral theory for non-Archimedean Banach spaces |
| title_full | Spectral integration and spectral theory for non-Archimedean Banach spaces |
| title_fullStr | Spectral integration and spectral theory for non-Archimedean Banach spaces |
| title_full_unstemmed | Spectral integration and spectral theory for non-Archimedean Banach spaces |
| title_short | Spectral integration and spectral theory for non-Archimedean Banach spaces |
| title_sort | spectral integration and spectral theory for non archimedean banach spaces |
| url | http://dx.doi.org/10.1155/S016117120201150X |
| work_keys_str_mv | AT sludkovsky spectralintegrationandspectraltheoryfornonarchimedeanbanachspaces AT bdiarra spectralintegrationandspectraltheoryfornonarchimedeanbanachspaces |