Weak* exactness for dual operator spaces

Zhe Dong, Zhong Jin Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a new tensor product over(⊗ :, σ, ∨) and study the weak* condition C, which is also called weak* exactness, for dual operator spaces. Our definition of weak* condition C is equivalent to Kirchberg's notion of weak exactness in the case of von Neumann algebras. We also study the connection of weak* exact W*-TROs with their linking von Neumann algebras and study the structure of exact (respectively, nuclear) W*-TROs.

Original languageEnglish (US)
Pages (from-to)373-397
Number of pages25
JournalJournal of Functional Analysis
Volume253
Issue number1
DOIs
StatePublished - Dec 1 2007

Keywords

  • Dual operator spaces
  • W-TROs
  • Weak exactness
  • von Neumann algebras

ASJC Scopus subject areas

  • Analysis

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