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.
|Number of pages||21|
|Journal||Integral Equations and Operator Theory|
|State||Published - Mar 1994|
- AMS (MOS) subject classifications: primary 47B05, 47B55, secondary 46A40