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Inequality involving norm of Dirac matrix

  1. Sep 26, 2012 #1

    I am reading a set of lecture notes on lattice QCD:

    There is an inequality here i do not understand. It is numbered (1.51)
    and reads:
    || (1-P) D^{-1} (1-P)|| \leq || (1-P) (D^{\dagger}D)^{-1} (1-P)||^{1/2}

    || ... || is the operator norm derived from the standard scalar product of Dirac

    P is an orthogonal projector to some arbitrary subspace.

    D is a discretized version of the Dirac-operator. It is assumed that D is invertible
    and it's eigenvalue spectrum is contained in a disk in the right half of the
    complex plane, with center M+m and radius M, m and M being positive real numbers.
    Nothing else is assumed of D.

    Any idea how this inequality can be derived? I don't see it...

  2. jcsd
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