Abstract
LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation λx=T x+y to possess a nonnegative solutionxεE wherey is a given nonnegative and nontrivial element ofE and λ is any given positive parameter.
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Jang-Lewis, RJ., Victory, H.D. On nonnegative solvability of linear operator equations. Integr equ oper theory 18, 88–108 (1994). https://doi.org/10.1007/BF01225214
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DOI: https://doi.org/10.1007/BF01225214