Systems formed by translates of one element in L p ( R ) L_{p}(mathbb R) Academic Article uri icon


  • Let 1 p < , f Lp(R), and R. We consider the closed subspace of Lp(R), Xp(f, ), generated by the set of translations f() of f by . If p = 1 and {f(): } is a bounded minimal system in L1(R), we prove that X1(f, ) embeds almost isometrically into 1. If {f(): } is an unconditional basic sequence in Lp(R), then {f(): } is equivalent to the unit vector basis of p for 1 p 2 and Xp(f, ) embeds into p if 2 < p 4. If p > 4, there exists f Lp(R) and Z so that {f(): } is unconditional basic and Lp(R) embeds isomorphically into Xp(f, ). 2011 American Mathematical Society.

published proceedings

  • Transactions of the American Mathematical Society

altmetric score

  • 3

author list (cited authors)

  • Odell, E., Sar, B., Schlumprecht, T. h., & Zheng, B.

citation count

  • 7

complete list of authors

  • Odell, E||Sarı, B||Schlumprecht, Th||Zheng, B

publication date

  • January 2011