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Journal of the London Mathematical Society 1981 s2-24(3):548-554; doi:10.1112/jlms/s2-24.3.548
© 1981 by London Mathematical Society
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© Oxford University Press

On the Domain Invariance Theorem for Accretive Mappings

Rainald Schöneberg

Osdorfer Landstrasse 311, 2000 Hamburg 55, West Germany

Let E be a Banach space. If D is a subset of E and R a mapping of D into E, then R is said to be accretive if and only if ||x – y|| ≤ ||(x – y) + t(R(x) – R(y))|| for all x, y {varepsilon} D and all t ≥ 0. Using only this defining property of accretive mappings, we give a straightforward and elementary proof of the important fact that T(U) is open, if U is an open subset of E and T : U -> E is continuous, locally closed, locally one to-one and locally accretive.


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