McIntosh formula for the gap between regular operators
The author gives an alternative definition for the gap between two complemented submodules of a Hilbert \(C^*\)-module using the distance concept as in the case of closed subspaces of a Banach space. He also derives the McIntosh formula for computing the gap of regular operators between Hilbert \(C^*\)-modules. The gap between two closed subspaces of a Hilbert space is defined as the norm of the difference of the orthogonal projections onto these subspaces. The same notion is applied to the graphs of operators to define the gap between two operators. This definition, as it involves projections, is not applicable for closed subspaces of a Banach space. In this case, it is defined in terms of the distance between a point and a subspace.
scientific article; zbMATH DE number 6147122
scientific article