Am-compact operator - Open Access .click

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Quaestiones Mathematicae, 2012
We introduce and study a new class of operators that we call b-AMcompact operators, and we establish necessary and sufficient conditions on the duality property for this class of operators. As interesting consequences, we obtain some characterizations of discrete KB-spaces.Keywords: Order continuous norm, b-AM-compact operator, KB-space, discrete ...
Abdelmonaim El Kaddouri +3 more
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Dedekind σ-complete vector lattice of b-AM-compact operators

Quaestiones Mathematicae, 2017
We give several equivalent conditions characterizing the case when Krb-AM(E,F) is Dedekind σ-complete. Moreover, we describe the case when the space of all regular b-AM-compact operators from E to F is complete under the b-AM-norm.Keywords: Banach lattices, b-AM-compact operator, discrete ...
На Ченг
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Some new results on the class of AM-compact operators

Rendiconti del Circolo Matematico di Palermo, 2010
An operator between Banach lattices is called \textit{AM-compact} if the image of each order interval \([-x,x]\), \(x\geq 0\), is norm relatively compact. In general, if \(T\) is AM-compact, its adjoint may not be AM-compact. Results relating the AM-compactness property of an operator to the AM-compactness property of its adjoint are provided.
Belmesnaoui Aqzzouz, Aziz Elbour
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The essential spectrum of AM-compact operators