Stability of diametral diameter two properties

Langemets, Johann; Pirk, Katriin

doi:10.1007/s13398-021-01038-y

Cited by 6 publications

(3 citation statements)

References 16 publications

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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%

Daugavet Property in Tensor Product Spaces

Zoca¹,

Tradacete²,

Villanueva³

2019

J. Inst. Math. Jussieu

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We study the Daugavet property in tensor products of Banach spaces. We show that L1(µ) ⊗ ε L1(ν) has the Daugavet property when µ and ν are purely non-atomic measures. Also, we show that X ⊗ π Y has the Daugavet property provided X and Y are L1-preduals with the Daugavet property, in particular spaces of continuous functions with this property. With the same tecniques, we also obtain consequences about roughness in projective tensor products as well as the Daugavet property of projective symmetric tensor products.2010 Mathematics Subject Classification. Primary 46B04; Secondary 46B20, 46B28.

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Section: Introductionmentioning

confidence: 55%

Daugavet Property in Tensor Product Spaces

Zoca¹,

Tradacete²,

Villanueva³

2019

J. Inst. Math. Jussieu

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“…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%

Daugavet Points in Projective Tensor Products

Dantas¹,

Jung²,

Zoca³

2021

The Quarterly Journal of Mathematics

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In this paper, we are interested in studying when an element z in the projective tensor product $X {\widehat{\otimes}_\pi} Y$ turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of $X {\widehat{\otimes}_\pi} Y$ having the Daugavet property implies the existence of a great amount of isometries from Y into X*. Having this in mind, we provide methods for constructing non-trivial Daugavet points in $X {\widehat{\otimes}_\pi} Y$. We show that C(K)-spaces are examples of Banach spaces such that the set of the Daugavet points in $C(K) {\widehat{\otimes}_\pi} Y$ is weakly dense when Y is a subspace of C(K)*. Finally, we present some natural results on when an elementary tensor $x \otimes y$ is a Daugavet point.

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“…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%

Daugavet points in projective tensor products

Dantas,

Jung,

Zoca

2021

Preprint

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In this paper, we are interested in studying when an element z in the projective tensor product X ⊗ π Y turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of X ⊗ π Y having the Daugavet property implies the existence of a great amount of isometries from Y into X * . Having this in mind, we provide methods for constructing non-trivial Daugavet points in X ⊗ π Y . We show that C(K)-spaces are examples of Banach spaces such that the set of the Daugavet points in C(K) ⊗ π Y is weakly dense when Y is a subspace of C(K) * . Finally, we present some natural results on when an elementary tensor x ⊗ y is a Daugavet point.

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Stability of diametral diameter two properties

Cited by 6 publications

References 16 publications

Daugavet Property in Tensor Product Spaces

Daugavet Property in Tensor Product Spaces

Daugavet Points in Projective Tensor Products

Daugavet points in projective tensor products

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