Proc. Amer. Math. Soc.

2021

DOI: 10.1090/proc/15448

|View full text |Cite

|

Sign up to set email alerts

|

The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet property

Vladimir Kadets¹

Help me understand this report

View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

0

Mentioning

0

Contrasting

0

Year Published

2021

2021

2024

2024

Publication Types

Select...

Article4

Book1

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 8 publications

References 8 publications

Supporting

0

Mentioning

0

Contrasting

0

Order By: Relevance

The Daugavet Equation: Linear and Nonlinear Recent Results

¹

,

²

,

³

et al. 2023

Mathematics Online First Collections

View full text Add to dashboard Cite

No abstract

The Daugavet Equation: Linear and Nonlinear Recent Results

¹

,

²

,

³

et al. 2023

Mathematics Online First Collections

View full text Add to dashboard Cite

No abstract

Diameter two properties in some vector-valued function spaces

¹

,

²

2021

View full text Add to dashboard Cite

No abstract

Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and $$\Delta $$-points

Cobollo,

Isert,

López-Pérez

et al. 2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

View full text Add to dashboard Cite

We prove that there exists an equivalent norm $$\left| \left| \left| \cdot \right| \right| \right| $$ · on $$L_\infty [0,1]$$ L ∞ [ 0 , 1 ] with the following properties: The unit ball of $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) contains non-empty relatively weakly open subsets of arbitrarily small diameter; The set of Daugavet points of the unit ball of $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) is weakly dense; The set of ccw $$\Delta $$ Δ -points of the unit ball of $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) is norming. We also show that there are points of the unit ball of $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) which are not $$\Delta $$ Δ -points, meaning that the space $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) fails the diametral local diameter 2 property. Finally, we observe that the space $$(L_\infty [0,1],\left| \left| \left| \cdot \right| \right| \right| )$$ ( L ∞ [ 0 , 1 ] , · ) provides both alternative and new examples that illustrate the differences between the various diametral notions for points of the unit ball of Banach spaces.

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Product

Browser Extension Assistant by scite Citation Statement Search Reference Check Visualizations Dashboards Explore Journals Explore Organizations Explore Funders Embedding Badge Embedding Citation Search Pricing

Resources

Blog Help & FAQ Accessibility Statement API Terms For Universities & Governments For Researchers For Publishers For Corporate, Pharma & Enterprise Author Marketing Become an Affiliate Get an organization trial or quote scite Data & Services

About

News & Press Careers Read our Paper Coverage

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Copyright © 2024 scite LLC. All rights reserved.

Made with 💙 for researchers

Part of the Research Solutions Family.