The Kagan characterization theorem on Banach spaces
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A. Kagan introduced classes of distributions 𝒟_m,k in m-dimensional space ℝ^m. He proved that if the joint distribution of m linear forms of n independent random variables belong to the class 𝒟_m,m-1 then the random variables are Gaussian. If m=2 then the Kagan theorem implies the well-known Darmois-Skitovich theorem, where the Gaussian distribution is characterized by the independence of two linear forms of n independent random variables. In the paper we describe Banach spaces where the analogue of the Kagan theorem is valid.
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