Gelfand numbers of operators with values in a Hilbert space (Q1118140)

If u is an operator from a Banach space X to a Banach space Y the Gelfand numbers \(\{c_ n\}^{\infty}_{n=1}\) of u are defined by \[ c_ n=\inf \{\| u|_ Z\| | Z\subset X,\quad co\dim Z<n\}. \] This paper is a study of certain inequalities involving the Gelfand numbers of operators with range in some Hilbert space. Applications to problems concerning numerical estimates in the geometric theory of Banach spaces are also given.