TY - JOUR

T1 - On nonnegative solvability of linear operator equations

AU - Jang-Lewis, Ruey Jen

AU - Victory, Harold Dean

N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

PY - 1994/3

Y1 - 1994/3

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0013512551&partnerID=8YFLogxK

U2 - 10.1007/BF01225214

DO - 10.1007/BF01225214

M3 - Article

AN - SCOPUS:0013512551

VL - 18

SP - 88

EP - 108

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -