## Abstract

Let L(H) be the ⁎-algebra of all bounded operators on an infinite dimensional Hilbert space H and let (I,‖⋅‖_{I}) be an ideal in L(H) equipped with a Banach norm which is distinct from the Schatten–von Neumann ideal L_{p}(H), 1≤p>2. We prove that I isomorphically embeds into an L_{p}-space L_{p}(R), 1≤p>2 (here, R is the hyperfinite II_{1}-factor) if its commutative core (that is, Calkin space for I) isomorphically embeds into L_{p}(0,1). Furthermore, we prove that an Orlicz ideal L_{M}(H)≠L_{p}(H) isomorphically embeds into L_{p}(R), 1≤p>2, if and only if it is an interpolation space for the Banach couple (L_{p}(H),L_{2}(H)). Finally, we consider isomorphic embeddings of (I,‖⋅‖_{I}) into L_{p}-spaces associated with arbitrary finite von Neumann algebras.

Original language | English (US) |
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Pages (from-to) | 473-546 |

Number of pages | 74 |

Journal | Advances in Mathematics |

Volume | 312 |

DOIs | |

State | Published - May 25 2017 |

Externally published | Yes |

## Keywords

- Banach space embeddings
- Noncommutative independence

## ASJC Scopus subject areas

- Mathematics(all)