On nonnegative solvability of linear operator equations

Ruey Jen Jang-Lewis, Harold Dean Victory

Research output: Contribution to journalArticle

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Abstract

Let E be a Banach lattice having order continuous norm. Suppose, moreover, T is a nonnegative reducible operator having a compact iterate and which maps E into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on general Lp-spaces. In particular, we provide necessary and sufficient conditions for the operator equation λx=Tx+y to possess a nonnegative solution xεE where y is a given nonnegative and nontrivial element of E and λ is any given positive parameter.

Original languageEnglish
Pages (from-to)88-108
Number of pages21
JournalIntegral Equations and Operator Theory
Volume18
Issue number1
DOIs
StatePublished - Mar 1994

Keywords

  • AMS (MOS) subject classifications: primary 47B05, 47B55, secondary 46A40

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