For Fr{ \'e}chet spaces E and F we write (E,F) \in { B} if every continuous linear operator from E to F is bounded. Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{ n}) is an unconditional basis. We obtain a necessary and sufficient condition for (E,F) \in { B} when F = \lambda^{ l}(B). We say that a triple (E,F,G) has the bounded factorization property and write (E,F,G) \in { BF} if each continuous linear operator T : E \longrightarrow G that factors over F is bounded. We extend some results in \cite{ Ter03} to l-K\"{ o}the spaces and obtain a sufficient condition for (E,\lambda^{ l_1}(A) \hat{ otimes}_{ pi} \lambda^{ l_2}(B), \lambda^{ l_3}(C)) \in { BF} when \lambda^{ l_1}(A) and \lambda^{ l_2}(B) are nuclear.
Categories: math.FA