Multipliers of the Hardy space H1and power bounded operators Academic Article uri icon


  • 2001, Instytut Matematyczny. All rights reserved. We study the space of functions : I such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors , in H such that (n) = Tn, This implies that the matrix ((i + j))i,j0is a Schur multiplier of B(2) or equivalently is in the space (1 1) *. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H 1 which we call " shift-bounded ". We show that there is a which is a " completely bounded " multiplier of H1, or equivalently for which ((i + j))i,j0is a bounded Schur multiplier of B(2), but which is not " shift-bounded " on H1. We also give a characterization of " completely shift-bounded " multipliers on H1

published proceedings

  • Colloquium Mathematicum

author list (cited authors)

  • Pisier, G.

citation count

  • 2

complete list of authors

  • Pisier, Gilles

publication date

  • January 2001