DOI: 10.24193/fpt-ro.2025.1.07

Authors: K. Fallahi, H. Ardakani and S. Rajavzade

Abstract: In this paper, using the Right topology, we introduce three new properties in Banach lattices: the so-called Right orthogonality, the Right WORTH property, and the non-strictly Right Opial condition (and also positive versions of them). Moreover, Banach lattices in which these three properties coincide with order continuity of the norm are characterized. As an application, we give some sufficient conditions under which a Banach lattice has the Right fixed point property (or, positive Right fixed point property). In particular, it is established that for a Banach space X and a suitable Banach lattice F, a Banach lattice ℳ ⊂ K(X,F) has the Right fixed point property (resp. positive Right fixed point property) if each evaluation operator ψ_y^* on ℳ is a pseudo weakly compact (resp. positive pseudo weakly compact) operator, where ψ_y^* : ℳ → X^* is defined by ψ_y^* (T)=T^*y^* for y^* ∈ F^* and T ∈ ℳ.

Key Words and Phrases: Right topology, weak fixed point property, WORTH property, non-strictly Opial condition, weak orthogonality.

2010 Mathematics Subject Classification: 47H10, 46A40, 46B05, 46B30.

Published on-line: February 1st, 2025.

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