Operator spaces with complete bases, lacking completely unconditional bases

Research output: Contribution to journalArticlepeer-review


We construct a Hilbertian operator space X such that the set of completely bounded operators on X consists of Hubert-Schmidt perturbations of a certain representation of the second dual to the James space. This space possesses an orthonormal basis (e i) such that all basis projections are completely contractive, yet any n-dimensional block subspace has complete unconditionality constant of at least c√n (c is a constant).

Original languageEnglish (US)
Pages (from-to)551-561
Number of pages11
JournalHouston Journal of Mathematics
Issue number2
StatePublished - 2006
Externally publishedYes


  • Basis
  • Operator space
  • The James space
  • Unconditional basis

ASJC Scopus subject areas

  • General Mathematics


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