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Thread: Rank of a projection (definition)

  1. #1
    Junior Member
    Feb 2010

    Rank of a projection (definition)

    If P is a linear operator between vector spaces, or a bounded linear operator between Banach spaces etc., its rank is defined as the dimension of the image.

    What exactly is the dimension of a projection (or more generally, an element, should it make sense) in an arbitrary C*-algebra (not necessarily of compact operators)?

    Thanks in advance

    [EDIT]: nevermind, I got it... dumb me
    Last edited by Nyrox; Nov 1st 2010 at 08:52 AM.
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