Injectivity of operator spaces

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Abstract

We study the structure of injective operator spaces and the existence and uniqueness of the injective envelopes of operator spaces. We give an easy example of an injective operator space which is not completely isometric to any C-algebra. This answers a question of Wittstock [23]. Furthermore, we show that an operator space E is injective if and only if there exists an injective C-algebra A and two projections p and q in A such that E is completely isometric to pAq.

Original languageEnglish (US)
Pages (from-to)89-104
Number of pages16
JournalTransactions of the American Mathematical Society
Volume315
Issue number1
DOIs
StatePublished - Sep 1989

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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