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Kato's inequality is shown for the magnetic relativistic Schrödinger operator H A,m defined as the operator theoretical square root of the selfadjoint, magnetic nonrelativistic Schrödinger operator (−i∇ − A(x)) 2 + m 2 with an L 2 loc vector potential A(x). ----------Mathematics Subject Classification (2010): 47A50; 81Q10; 47B25; 47N50; 47D06; 47D08.doi:10.4171/prims/53-1-3 fatcat:6xrnu4dwivc5lfkjcvwzgdhere