Abstract
This chapter is devoted to the so-called Vishik spectral theorem for bounded linear operators. Here, we mainly follow Attimu [4], Attimu and Diagana [3], Baker [7], and Vishik [54].
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D. Attimu, T. Diagana, Functional calculus for a class of unbounded linear operators on some non-Archimedean Banach spaces. Comment. Math. Univ. Carolin. 50(1), 37–60 (2009)
D. Attimu, Linear operators on some non-archimedean Hilbert spaces and their spectral theory. PhD Thesis, Howard University, Washington DC (2008)
R. Baker, A certain p-adic spectral theorem (2007). arXiv.math /070353901 [MATH.FA]
N. Koblitz, p-adic Analysis: A Short Course on Recent Work (Cambridge University Press, Cambridge, 1980)
M. Vishik, Non-archimedean spectral theory. J. Sov. Math. 30, 2513–2554 (1985)
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Diagana, T., Ramaroson, F. (2016). The Vishik Spectral Theorem. In: Non-Archimedean Operator Theory. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27323-5_4
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DOI: https://doi.org/10.1007/978-3-319-27323-5_4
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