Kato's Inequality for Magnetic Relativistic Schr\"odinger Operators

Kato’s inequality is shown for the magnetic relativistic Schr"odinger operator $H_{A,m}$ defined as the operator theoretical {\it square root} of the selfadjoint, magnetic nonrelativistic Schr"odinger operator $(-i\mathrm{\nabla }-A(x){)}^2+m^2$ with an $L_{\text{loc}}^2$ vector potential $A(x)$.