Criteria for the nuclearity of spaces of functions of infinitely many variables

AbstractThe present paper evolves from Berezanskii and Gali (Ukrainian Math. J. 24 (4) (1972), 435–464) and Berezanskii, Gali, and Zuk (Soviet. Math. Dokl. 13 (2) (1972)), in which, it was shown how one can construct a weighted infinite tensor product He,δ = ⊗n = 1:e,δ∞ = Hτn of Hilbert spaces Hτn with a given stabilizing sequence δ = (δn)n = 1∞(δn > 0). Here a weighted infinite tensor product ϑe = ⊗n = 1,e∞ϑn of nuclear spaces ϑn is established first. Criteria for nuclearity of the constructed spaces are also given. Some examples of nuclear spaces of functions of infinite many variables K(T∞) and A(T∞) are obtained