Embeddings of operator ideals into Lp-spaces on finite von Neumann algebras

M. Junge, F. Sukochev, D. Zanin

Research output: Contribution to journalArticlepeer-review

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 Lp(H), 1≤p>2. We prove that I isomorphically embeds into an Lp-space Lp(R), 1≤p>2 (here, R is the hyperfinite II1-factor) if its commutative core (that is, Calkin space for I) isomorphically embeds into Lp(0,1). Furthermore, we prove that an Orlicz ideal LM(H)≠Lp(H) isomorphically embeds into Lp(R), 1≤p>2, if and only if it is an interpolation space for the Banach couple (Lp(H),L2(H)). Finally, we consider isomorphic embeddings of (I,‖⋅‖I) into Lp-spaces associated with arbitrary finite von Neumann algebras.

Original languageEnglish (US)
Pages (from-to)473-546
Number of pages74
JournalAdvances in Mathematics
Volume312
DOIs
StatePublished - May 25 2017
Externally publishedYes

Keywords

  • Banach space embeddings
  • Noncommutative independence

ASJC Scopus subject areas

  • Mathematics(all)

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