On extensions of J-skew-symmetric and J-isometric operators

Abstract

In this paper it is proved that each densely defined J -skew-symmetric operator (or each J -isometric operator with D(A) = R(A) = H ) in a separable Hilbert space H has a J skew-self-adjoint (respectively J -unitary) extension in a separable Hilbert space H ⊇ H . We follow the ideas of Galindo in [A. Galindo, On the existence of J -self-adjoint extensions of J -symmetric operators with adjoint, Comm. Pure Appl. Math., Vol. XV, 423–425 (1962)] with necessary modifications. Mathematics subject classification (2010): 47A20.