A Banach space with,up to equivalence,precisely two symmetric bases

It is well know that the classical sequence spaces c_o andl _p (1≦p<∞) have, up to equivalence, just one symmetric basis. On the other hand, there are examples of Orlicz sequence spaces which have uncountably many mutually non-equivalent symmetric bases. Thus in 4], p. 130, the question is asked whether there is a Banach space with, up to equivalence, more than one symmetric basis, but not uncountably many. In this paper we answer the question positively, by exhibiting a Banach space with, up to equivalence, precisely two symmetric bases.