Archiv der Mathematik

, Volume 97, Issue 2, pp 151–156 | Cite as

On weakly injective von Neumann algebras



A von Neumann algebra \({M\subset B(H)}\) is called weakly injective if there exist an ultraweakly dense unital C*-subalgebra \({A\subset M}\) and a unital completely positive map φ : B(H) → M such that φ(a) = a for all \({a\in A}\). In this note we present several properties of weakly injective von Neumann algebras and highlight the role these algebras play in relation to the QWEP conjecture.

Mathematics Subject Classification (2000)

46L05 46L06 46L10 


C*-algebra von Neumann algebra Weakly injective QWEP conjecture 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceWagner CollegeStaten Island, New YorkUSA

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