Based on a couple of references, it seems that the answer is yes, see for example Boneta-Dierolf, 1992 and Bierstedt-Bonet, 1989.
However, from a comment to the answer of this MO question, I infer that there is a counterexample.
Based on a couple of references, it seems that the answer is yes, see for example Boneta-Dierolf, 1992 and Bierstedt-Bonet, 1989.
However, from a comment to the answer of this MO question, I infer that there is a counterexample.