Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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

http://luscher.web.cern.ch/luscher/lectures/LesHouches09.pdf

There is an inequality here i do not understand. It is numbered (1.51)

and reads:

[tex]

|| (1-P) D^{-1} (1-P)|| \leq || (1-P) (D^{\dagger}D)^{-1} (1-P)||^{1/2}

[/tex]

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

fields.

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...

Thanks...

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inequality involving norm of Dirac matrix

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**