A polynomially bounded operator on Hilbert space which is not similar to a contraction Academic Article uri icon

abstract

  • Let > 0. We prove that there exists an operator T : l2 l2 such that for any polynomial P we have ||P(T)|| (1 + )||P||, but T is not similar to a contraction, i.e. there does not exist an invertible operator S : l2 l2 such that \S-1TS|| 1. This answers negatively a question attributed to Halmos after his well-known 1970 paper ("Ten problems in Hilbert space"). We also give some related finite-dimensional estimates.

published proceedings

  • JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Pisier, G.

citation count

  • 63

complete list of authors

  • Pisier, G

publication date

  • April 1997