Ideals, Faces and Compressions

  • Erik M. Alfsen
  • Frederic W. Shultz
Part of the Mathematics: Theory & Applications book series (MTA)


In this chapter we will establish the connection between projections, ideals and faces in C*-algebras and von Neumann algebras. In the first two sections we will explain how projections and ideals are related to each other, and to faces of the normal state space in the von Neumann algebra case, and to faces of the state space in the C*-algebra case. In the next section we will relate projections and ideals to invariant subspaces of the predual of a von Neumann algebra and the dual of a C*-algebra. In the last section we will give an order theoretic characterization of compressions of a von Neumann algebra, i.e., maps of the form apap where p is a projection.


Invariant Subspace Left Ideal Positive Cone Central Projection Polar Decomposition 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Erik M. Alfsen
    • 1
  • Frederic W. Shultz
    • 2
  1. 1.Mathematical InstituteUniversity of OsloOsloNorway
  2. 2.Department of MathematicsWellesley CollegeWellesleyUSA

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