On piositive invertibility and splittings of operators in ordered Banach spaces

Sivakumar K. C. , Weber M. R.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 1.

Abstract:
The positive invertibility of operators between Banach spaces, ordered by special closed cones, is characterized by the existence of splittings for the operators into the difference of two operators with appropriate spectral properties. Some results, up to now known only for matrices, are generalized to operators and to order intervals of operators.

Keywords: ordered Banach spaces, cones in ordered spaces, positively invertible operators, splitting of operators, intervals of operators

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