2021
DOI: 10.1007/s13398-021-01038-y
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Stability of diametral diameter two properties

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Cited by 6 publications
(3 citation statements)
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“…Moreover, the main theorem in the section is Theorem 4.3, where we prove that X ⊗ π Y has the DD2P whenever X has the WODP and Y is any Banach space. In addition to represent a progress on the open questions [12,Question 4.2] and [2, Section 5, (b)], the above result improves [14,Proposition 5.2], where the authors obtained a weaker thesis under the same assumptions (see Remark 4.6 for details).…”
Section: Introductionmentioning
confidence: 55%
“…Moreover, the main theorem in the section is Theorem 4.3, where we prove that X ⊗ π Y has the DD2P whenever X has the WODP and Y is any Banach space. In addition to represent a progress on the open questions [12,Question 4.2] and [2, Section 5, (b)], the above result improves [14,Proposition 5.2], where the authors obtained a weaker thesis under the same assumptions (see Remark 4.6 for details).…”
Section: Introductionmentioning
confidence: 55%
“…We finish this section by presenting a short but detailed study of elementary tensors x ⊗ y in X ⊗ π Y which are Daugavet points. This is motivated by the recent paper [14], where the authors prove that if x ∈ S X is a ∆-point, then x ⊗ y ∈ S X ⊗ π Y is a ∆-point for every y ∈ S Y (see [14,Remark 5.4]). We recall that x ∈ S X is a ∆-point if given ε > 0 and a slice S of B X containing x, then there exists y ∈ S satisfying x − y 2 − ε.…”
Section: The Resultsmentioning
confidence: 99%
“…We finish this section by presenting a short but detailed study of elementary tensors x ⊗ y in X ⊗ π Y which are Daugavet points. This is motivated by the recent paper [13], where the authors prove that if x ∈ S X is a ∆-point, then x ⊗ y ∈ S X ⊗ π Y is a ∆-point for every y ∈ S Y (see [13,Remark 5.4]). We recall that x ∈ S X is a ∆-point if given ε > 0 and a slice S of B X containing x, then there exists y ∈ S satisfying x − y 2 − ε.…”
Section: The Resultsmentioning
confidence: 99%