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(1.2) ajak+akaj=2djkl (/, fe = l, 2, 3, 4). We denote by HQ the operator H with We denote by and | | the usual inner product and norm in C, respectively, and by ( , ) and || || the inner product and norm in the Hilbert space «#=[L2CR )II, respectively. We also denote by | | and || || the operator norm of a 4x4 matrix and a bounded linear operator in «#, respectively. We denote by / the 4x4 identity matrix, which at times implies the 2x2 identity matrix, but no confusion will occur. For a closable operator T in JC, we denote by T its closure. For an (formal) operator T, we denote by T the restriction of T to the domain

On essential selfadjointness, distinguished selfadjoint extension and essential spectrum of Dirac operators with matrix valued potentials