ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACES AND APPLICATION

Simultaneous contractifications, simultaneous proper contractifications and semigroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for a single bounded linear operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFrechet differentiable at that point.