On regular riesz operators

  • Heinrich Raubenheimer Department of Mathematics and Applied Mathematics, University of the Orange Free State, PO Box 339, Bloemfontein 9300, South Africa; Present address: Department of Mathematics, Rand Afrikaans University, PO Box 524, Auckland Park 2006, South Africa


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

Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606