Delta- and Daugavet points in Banach spaces. Issue 2 (27th May 2020)
- Record Type:
- Journal Article
- Title:
- Delta- and Daugavet points in Banach spaces. Issue 2 (27th May 2020)
- Main Title:
- Delta- and Daugavet points in Banach spaces
- Authors:
- Abrahamsen, T. A.
Haller, R.
Lima, V.
Pirk, K. - Abstract:
- Abstract: A Δ-point x of a Banach space is a norm-one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance 2 from x . If, in addition, every point in the unit ball is arbitrarily close to such convex combinations, x is a Daugavet point. A Banach space X has the Daugavet property if and only if every norm-one element is a Daugavet point. We show that Δ- and Daugavet points are the same in L 1 -spaces, in L 1 -preduals, as well as in a big class of Müntz spaces. We also provide an example of a Banach space where all points on the unit sphere are Δ-points, but none of them are Daugavet points. We also study the property that the unit ball is the closed convex hull of its Δ-points. This gives rise to a new diameter-two property that we call the convex diametral diameter-two property. We show that all C ( K ) spaces, K infinite compact Hausdorff, as well as all Müntz spaces have this property. Moreover, we show that this property is stable under absolute sums.
- Is Part Of:
- Proceedings of the Edinburgh Mathematical Society. Volume 63:Issue 2(2020)
- Journal:
- Proceedings of the Edinburgh Mathematical Society
- Issue:
- Volume 63:Issue 2(2020)
- Issue Display:
- Volume 63, Issue 2 (2020)
- Year:
- 2020
- Volume:
- 63
- Issue:
- 2
- Issue Sort Value:
- 2020-0063-0002-0000
- Page Start:
- 475
- Page End:
- 496
- Publication Date:
- 2020-05-27
- Subjects:
- diametral diameter-two property, -- Daugavet property, -- L1-space, -- L1-predual space, -- Müntz space
46B20, -- 46B04, -- 46B22
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=PEM ↗
- DOI:
- 10.1017/S0013091519000567 ↗
- Languages:
- English
- ISSNs:
- 0013-0915
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library STI - ELD Digital store
- Ingest File:
- 15274.xml