| MSC: | 47H04 | Set-valued operators [See also 28B20, 54C60, 58C06] |
| 47H09 | Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. | |
| 65JXX | Numerical analysis in abstract spaces |
Abstract:
In the study of iterative methods used to solve linear operator equations
sequences of linear iteration operators $(T_k)$ occur which have a nontrivial projection kernel,
that is a linear projector $P \neq O$ satisfying $P = T_k P = P T_k$ for all natural $k$.
The convergence proof for $(T_k)$ or some related operator sequences is simplified if such $P$ is known.
It is investigated when projection kernels exist and how they can be determined. Besides, special
types of projection kernels are considered.