  This paper is concerned with the stability of deficiency indices of Hermitian
subspaces (i.e., linear relations) under relatively bounded perturbations in
Hilbert spaces. Several results about invariance of deficiency indices of
Hermitian subspaces under relatively bounded perturbations are established. As
a consequence, invariance of self-adjointness of Hermitian subspaces under
relatively bounded perturbations is obtained. In addition, it is shown that the
deficiency indices may shrink in the special case that the relative bound is
equal to 1. The results obtained in the present paper generalize the
corresponding results for symmetric operators to more general Hermitian
subspaces.
