Abstract:The diametral dimension, ∆(E), and the approximate diametral dimension, δ(E), of a nuclear Fréchet space E which satisfies DN and Ω, is related to power series spaces Λ 1 (ε) and Λ ∞ (ε) for some exponent sequence ε. In this article, we examine a question of whether δ(E) must coincide with that of a power series space if ∆(E) does the same, and vice versa.In this regard, we first show that this question has an affirmative answer in an infinite type case by proving the fact that ∆(E) = ∆ (Λ ∞ (ε)) if and only i… Show more
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