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Search: MSC category 46B42 ( Banach lattices [See also 46A40, 46B40] )

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1. CMB 2011 (vol 56 pp. 434)

Wnuk, Witold
Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces
Following ideas used by Drewnowski and Wilansky we prove that if $I$ is an infinite dimensional and infinite codimensional closed ideal in a complete metrizable locally solid Riesz space and $I$ does not contain any order copy of $\mathbb R^{\mathbb N}$ then there exists a closed, separable, discrete Riesz subspace $G$ such that the topology induced on $G$ is Lebesgue, $I \cap G = \{0\}$, and $I + G$ is not closed.

Keywords:locally solid Riesz space, Riesz subspace, ideal, minimal topological vector space, Lebesgue property
Categories:46A40, 46B42, 46B45

2. CMB 2011 (vol 54 pp. 577)

Aqzzouz, Belmesnaoui
Erratum: The Duality Problem For The Class of AM-Compact Operators On Banach Lattices
It is proved that if a positive operator $S: E \rightarrow F$ is AM-compact whenever its adjoint $S': F' \rightarrow E'$ is AM-compact, then either the norm of F is order continuous or $E'$ is discrete. This note corrects an error in the proof of Theorem 2.3 of B. Aqzzouz, R. Nouira, and L. Zraoula, The duality problem for the class of AM-compact operators on Banach lattices. Canad. Math. Bull. 51(2008).

Categories:46A40, 46B40, 46B42

3. CMB 2008 (vol 51 pp. 15)

Aqzzouz, Belmesnaoui; Nouira, Redouane; Zraoula, Larbi
The Duality Problem for the Class of AM-Compact Operators on Banach Lattices
We prove the converse of a theorem of Zaanen about the duality problem of positive AM-compact operators.

Keywords:AM-compact operator, order continuous norm, discrete vector lattice
Categories:46A40, 46B40, 46B42

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