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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120201150X |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |