On resolvent positive operators and positive \(C_ 0\)-semigroups on AL- spaces. (English) Zbl 0686.47040
The paper contains a new proof of the following result of Desch.
Let E be a Banach lattice with the additional property \(\| x+y\| =\| x\| \| y\|.\) Let A be the generator of a positive \(C_ 0\)-semigroup on E. Let B: D(A)\(\to E\) be a positive operator and assume that \(A+B\) is resolvent positive. Then \(A+B\) is the generator of a positive \(C_ 0\)-semigroup.
Let E be a Banach lattice with the additional property \(\| x+y\| =\| x\| \| y\|.\) Let A be the generator of a positive \(C_ 0\)-semigroup on E. Let B: D(A)\(\to E\) be a positive operator and assume that \(A+B\) is resolvent positive. Then \(A+B\) is the generator of a positive \(C_ 0\)-semigroup.
Reviewer: J.de Graaf
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