Projective descriptions of the (LF)-spaces of type LB(λp(A), F)

Abstract

AbstractLet 1 < p < + ∞ or p = 0 and let A = (an)n be an increasing sequence of strictly positive weights on I. Let F be a Fréchet space. It is proved that if λp(A) satisfies the density condition of Heinrich and a certain condition (Ct) holds, then the (LF)-space LBi(λp(A), F) is a topological subspace of Lb(λp(A), F). It is also proved that these conditions are necessary provided F = λq(A) or F contains a complemented copy of Iq with 1 < p ≤ q < +∞.