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Spectral integration and spectral theory for non-Archimedean Banach spaces

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  • S. Ludkovsky
  • B. Diarra

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.

Suggested Citation

  • S. Ludkovsky & B. Diarra, 2002. "Spectral integration and spectral theory for non-Archimedean Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-22, January.
    • Handle: RePEc:hin:jijmms:459262
    DOI: 10.1155/S016117120201150X
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    Cited by:

    1. Sergey V. Ludkowski, 2019. "Normed Dual Algebras," Mathematics, MDPI, vol. 7(2), pages 1-14, February.
    2. Sergey V. Ludkowski, 2019. "Structure of Normed Simple Annihilator Algebras," Mathematics, MDPI, vol. 7(4), pages 1-10, April.

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