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Quaestiones Mathematicae

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On regular riesz operators

Heinrich Raubenheimer

Abstract


The r-asymptotically quasi finite rank operators on Banach lattices are examples of regular Riesz operators. We characterise Riesz elements in a subalgebra of a Banach algebra in terms of Riesz elements in the Banach algebra. This enables us to characterise r-asymptotically quasi finite rank operators in terms of adjoint operators. The r-asymptotically quasi finite rank operators are also employed to study the following problem: Suppose operators S and T on a Banach lattice E satisfy 0 ≤ ST. If T is a Riesz operator, when is it true that S is a Riesz operator?

Quaestiones Mathematicae 23(2000), 179–186



http://dx.doi.org/10.2989/16073600009485966
AJOL African Journals Online