Vector-valued Eidelheit sequences and the non B-completeness of tensor   products
  We introduce vector-valued Eidelheit sequences and obtain a characterization that generalizes Eidelheit's classical theorem (Studia Math. 6 (1936), 139-148). As an application, we discuss criteria for non $B$-completeness of completed tensor products. 
Andreas Debrouwere and Jasson Vindas
math.FA