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• W1419489776 abstract "In this paper, we study weak stability properties of an ε-isometry defined on a wedge W of a Banach space X, instead of the whole space X. As a result, we show that if f:W→Y is an ε-isometry with f(0)=0 for some Banach space Y, then there exists a w⁎-compact absolutely convex set B⊂BX⁎ satisfying that (a) p(x)≡supx⁎∈B⁡〈x⁎,x〉=‖x‖ for all x∈W∪−W; and (b) for every x⁎∈B, there is ϕ∈BY⁎ so that|〈ϕ,f(x)〉−〈x⁎,x〉|≤2ε,for all x∈W. This is a generalization of a recent result so called a universal theorem for stability of ε-isometries (but the proof is more technical). As its application, we prove that if the ε-isometry f is defined on the positive cone W of a C(K)-space, or, an abstract M-space with a strong unit (in particular, ℓ∞(Γ), and L∞(μ) for a finite measure μ), then we can choose the set B to be BX⁎; the closed unit ball of the dual X⁎; and further show that X⁎⁎ is w⁎-to-w⁎ continuously isometric to a subspace of Y⁎⁎." @default.
• W1419489776 created "2016-06-24" @default.
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• W1419489776 date "2016-01-01" @default.
• W1419489776 modified "2023-10-18" @default.
• W1419489776 title "On weak stability of ε-isometries on wedges and its applications" @default.
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• W1419489776 doi "https://doi.org/10.1016/j.jmaa.2015.08.033" @default.
• W1419489776 hasPublicationYear "2016" @default.
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