Mathematische Annalen

, Volume 324, Issue 2, pp 277–327

Hankel and Toeplitz–Schur multipliers

  • A.B. Aleksandrov
  • V.V. Peller
Original article

DOI: 10.1007/s00208-002-0339-z

Cite this article as:
Aleksandrov, A. & Peller, V. Math Ann (2002) 324: 277. doi:10.1007/s00208-002-0339-z

Abstract.

We study the problem of characterizing Hankel–Schur multipliers and Toeplitz–Schur multipliers of Schatten–von Neumann class \({\boldsymbol S}_p\) for \(0<p<1\). We obtain various sharp necessary conditions and sufficient conditions for a Hankel matrix to be a Schur multiplier of \({\boldsymbol S}_p\). We also give a characterization of the Hankel–Schur multipliers of \({\boldsymbol S}_p\) whos e symbols have lacunary power series. Then the results on Hankel–Schur multipliers are used to obtain a characterization of the Toeplitz–Schur multipliers of \({\boldsymbol S}_p\). Finally, we return to Hankel–Schur multipliers and obtain new results in the case when the symbol of the Hankel matrix is a complex measure on the unit circle.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A.B. Aleksandrov
    • 1
  • V.V. Peller
    • 2
  1. 1.St-Petersburg Branch, Steklov Institute of Mathematics, Fontanka 27, 191011 St-Petersburg, Russia RU
  2. 2.Department of Mathematics, Michigan State University, East Lansing, MI 66506, USA US