Diametral dimensions of Fréchet spaces

This article provides new results concerning the equality between two diametral dimensions. It shows that this equality is true for hilbertizable Fréchet-Schwartz spaces. Moreover, it studies the notion of prominent sets of Terzioglu and proves that the property "omega bar" of Vogt and Wagner implies the existence of prominent sets. Finally, it shows that the converse implication is true for regular Köthe sequence spaces and brings some spaces with prominent sets but which do not verify “omega bar” (among which there is the space H(D) x H(C)).