Self-adjointness of the dirac operator in a space of vector functions

V. A. Bezverkhnii

M. V. Lomonosov Moscow State University

Abstract: This paper is devoted to the proof of the self-adjointness of the minimal operator defined on the space $L_2(-\infty,\infty;H)$ ($H$ being a separable Hilbert space) by the expression $l=iJ\frac d{dt}+A+B(t)$. The coefficients in this expression are self-adjoint operators on $H$, with $A$ being unbounded, $AJ+JA=0$, and the function $\|B(t)\|_H$ being assumed to lie in $L_2^{\operatorname{loc}}(-\infty,\infty)$. The result obtained is applicable to the Dirac operator.

UDC: 517

Received: 23.04.1974

 English version: Mathematical Notes, 1975, 18:1, 583–585

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