### Abstract

Suppose A is a von Neumann algebra with a normal faithful normalized trace T. We prove that if Eis a homogeneous Hilbertian subspace of L_{P}(T) (1 ≤ p < ∞) such that the norms induced on E by L_{p} (τ) and L_{2}(τ) are equivalent, then E is completely isomorphic to the subspace of L_{p}([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous subspace of L_{p}(τ) is completely isomorphic to the span of Rademacher functions in L_{p}([0, 1]). In particular, this applies to the linear span of operators satisfying the canonical anti-commutation relations. We also show that the real interpolation space (R, C)_{θ,p} embeds completely isomorphically into L_{p}(R.) (R is the hyperfinite II_{1} factor) for any 1 ≤ p < 2 and θ ε (0, 1). Indiana University Mathematics Journal

Original language | English (US) |
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Pages (from-to) | 733-766 |

Number of pages | 34 |

Journal | Indiana University Mathematics Journal |

Volume | 56 |

Issue number | 2 |

DOIs | |

State | Published - Jun 6 2007 |

### Keywords

- Completely unconditional bases
- Homogenous hilbertian spaces
- Noncommutative L spaces

### ASJC Scopus subject areas

- Mathematics(all)