ON THE DEFECT INDICES OF LINEAR OPERATORS IN BANACH SPACE AND ON SOME GEOMETRIC QUESTIONS

Abstract : The authors show that the theory of defect indices of Hermitian operators in a Hilbert space can be extended to the case of linear operators in a Banach space. For this purpose they use the idea of aperture (gap) of two sub-spaces with whose help it is convenient to establish in many cases the equality of the dimensions of the subspaces of the Banach space. The authors also arrive at several geometric conjectures.