UNCONDITIONAL SCHAUDER FRAMES OF TRANSLATES IN Lp(Rd)

We show that, for 1 p(Double-struck capital R-d) does not admit unconditional Schauder frames {f(i, f ' i)}i is an element of N where {f(i)} is a sequence of translates of finitely many functions and {f ' i} is seminormalized. In fact, the only subspaces of L-p(Double-struck capital R-d) admitting such Banach frames are those isomorphic to lp. On the other hand, if 2 i}(i is an element of N)subset of Double-struck capital R(d)is an unbounded sequence, there is a subsequence {lambda(i)}(i is an element of N), a function f is an element of L-p(Double-struck capital R-d), and a seminormalized sequence of bounded functionals {lambda '(i)}(i is an element of N)such that{T lambda mif,fi '}(i is an element of N) is an unconditional Schauder frame for L-p(Double-struck capital R-d).