Spectral integration and spectral theory for non-Archimedean Banach spaces

S. Ludkovsky and B. Diarra

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-22

Abstract:

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 ( A ˆ , μ , 𝕂 ) -projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:459262

DOI: 10.1155/S016117120201150X

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