DOI: 10.24193/fpt-ro.2025.2.03

Authors: H. Ardakani, K. Fallahi and F. Norouzi

Abstract: Using weakly p-summable and Dunford-Pettis (resp. weakly p-summable and almost Dunford-Pettis) sequences, some geometric properties on Banach lattices are studied. Moreover, by the concept of relatively compact Dunford-Pettis property (briefly, DP_rcP) and strong DP_rcP, Banach lattices in which some of these properties coincide are characterized. As an application, Banach lattices with the Right fixed point property of order p are considered. 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 of order p (resp. strong Right fixed point property of order p) if each evaluation operator ψ_y^* on ℳ is Dunford-Pettis p-convergent (resp. almost Dunford-Pettis p-convergent), 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, fixed point property, weak orthogonality, Dunford-Pettis set, almost Dunford-Pettis set.

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

Published on-line: May 1st, 2025.

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