Multiplication operators on L(L-p) and l(p)-strictly singular operators Academic Article uri icon


  • A classification of weakly compact multiplication operators on L(L p), 1 < p < , is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of l p-strictly singular operators, and we also investigate the structure of general lp-strictly singular operators on Lp. The main result is that if an operator T on Lp, 1 < p < 2, is l p-strictly singular and T|x is an isomorphism for some subspace X of Lp, then X embeds into Lr for all r < 2, but X need not be isomorphic to a Hilbert space. It is also shown that if T is convolution by a biased coin on Lp of the Cantor group, 1 p < 2, and T|x is an isomorphism for some reflexive subspace X of L p, then X is isomorphic to a Hilbert space. The case p = 1 answers a question asked by Rosenthal in 1976. European Mathematical Society 2008.

published proceedings


author list (cited authors)

  • Johnson, W. B., & Schechtman, G.

citation count

  • 7

complete list of authors

  • Johnson, William B||Schechtman, Gideon

publication date

  • January 2008