Relative surjectivity coefficients of linear operators (Q1589051)

The paper deals with certain characteristics of linear operators between Banach spaces which measure the degree of surjectivity and injectivity. Two numerical coefficients are well known: the surjectivity coefficient and the modulus of injectivity [see \textit{A. Pietsch}, Operator Ideals, Berlin (1978; Zbl 0399.47039)]. The author introduces natural generalizations: the relative coefficient of surjectivity and the relative modulus of injectivity. It is shown that these numerical characteristics are useful for obtaining an estimate for the infimum of norms of bounded operators which are generalized-inverses to a linear operator.