Integral Equations and Operator Theory

, Volume 18, Issue 1, pp 88–108

On nonnegative solvability of linear operator equations

  • Ruey-Jen Jang-Lewis
  • Harold Dean VictoryJr.
Article

DOI: 10.1007/BF01225214

Cite this article as:
Jang-Lewis, RJ. & Victory, H.D. Integr equ oper theory (1994) 18: 88. doi:10.1007/BF01225214

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 generalLp-spaces. In particular, we provide necessary and sufficient conditions for the operator equation λx=Tx+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 

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Ruey-Jen Jang-Lewis
    • 1
  • Harold Dean VictoryJr.
    • 1
  1. 1.Department of MathematicsTexas Tech UniversityLubbockUSA

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