Integral Equations and Operator Theory

, Volume 18, Issue 1, pp 88-108

First online:

On nonnegative solvability of linear operator equations

  • Ruey-Jen Jang-LewisAffiliated withDepartment of Mathematics, Texas Tech University
  • , Harold Dean VictoryJr.Affiliated withDepartment of Mathematics, Texas Tech University

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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.

AMS (MOS) subject classifications

primary 47B05 47B55 secondary 46A40