Random Series of Trace Class Operators Academic Article uri icon


  • In this lecture, we present some results on Gaussian (or Rademacher) random series of trace class operators, mainly due jointly with F. Lust-Piquard. We will emphasize the probabilistic reformulation of these results, as well as the open problems suggested by them. We start by a brief survey of what is known about the problem of characterizing a.s. convergent (Gaussian or Rademacher) series of random vectors in a Banach space. The main result presented here is that for certain pairs of Banach spaces $E,F$ that include Hilbert spaces (and type 2 spaces with the analytic UMD property), we have $$ R(Ehatotimes F) =R(E)hatotimes F + Ehatotimes R(F) $$ where $R(E)$ denotes the space of convergent Rademacher series with coefficients in $E$ and $Ehatotimes F$ denotes the projective tensor product.

published proceedings

  • Proceedings Cuarto CLAPEM Mexico 1990. Contribuciones en probabilidad y estadistica matematica (1992) 29-42

author list (cited authors)

  • Pisier, G.

complete list of authors

  • Pisier, Gilles

publication date

  • March 2011