Strictly regular echelon Köthe spaces (Q1063203)

We give a slighty more concrete definition of a strictly regular Fréchet space that was introduced by \textit{D. N. Zarnadze} [Math. Notes 31, 454-458 (1982; Zbl 0562.46001)], and we prove that a strictly regular echelon Köthe space \(\Lambda^ p(X,\beta,\mu,g_ k)\) must be isomorphic to a countable product of \(L^ p(d\upsilon)\)-spaces, - i.e., must be trivial -. A pseudo-converse of this implication has been proved also.