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

Invariance of deficiency indices of Hermitian subspaces under relatively bounded perturbations