scholarly journals Quotients of Banach Spaces with the Daugavet Property

2008 ◽  
Vol 56 (2) ◽  
pp. 131-147 ◽  
Author(s):  
Vladimir Kadets ◽  
Varvara Shepelska ◽  
Dirk Werner
Keyword(s):  
Banach Spaces ◽  
Daugavet Property

scholarly journals L-orthogonality, octahedrality and Daugavet property in Banach spaces

2021 ◽  
Vol 383 ◽  
pp. 107719
Author(s):  
Ginés López-Pérez ◽  
Abraham Rueda Zoca
Keyword(s):  
Banach Spaces ◽  
Daugavet Property

scholarly journals Banach spaces with the Daugavet property, and the centralizer

2008 ◽  
Vol 254 (8) ◽  
pp. 2294-2302 ◽  
Author(s):  
Julio Becerra Guerrero ◽  
Angel Rodríguez-Palacios
Keyword(s):  
Banach Spaces ◽  
Daugavet Property

scholarly journals Delta- and Daugavet points in Banach spaces

2020 ◽  
Vol 63 (2) ◽  
pp. 475-496
Author(s):  
T. A. Abrahamsen ◽  
R. Haller ◽  
V. Lima ◽  
K. Pirk
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Unit Ball ◽  
Banach Spaces ◽  
Unit Sphere ◽  
Closed Convex Hull ◽  
Müntz Spaces ◽  
Daugavet Property ◽  
Diameter Two Property

AbstractA 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 L1-spaces, in L1-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.

scholarly journals ALMOST ISOMETRIC IDEALS IN BANACH SPACES

2013 ◽  
Vol 56 (2) ◽  
pp. 395-407 ◽  
Author(s):  
TROND A. ABRAHAMSEN ◽  
VEGARD LIMA ◽  
OLAV NYGAARD
Keyword(s):  
Banach Spaces ◽  
Natural Class ◽  
Daugavet Property

AbstractA natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property. Lindenstrauss spaces are known to be the class of Banach spaces that are ideals in every superspace; we show that being an almost isometric ideal in every superspace characterizes the class of Gurariy spaces.

scholarly journals DAUGAVET PROPERTY IN TENSOR PRODUCT SPACES

2019 ◽  
pp. 1-20 ◽  
Author(s):  
Abraham Rueda Zoca ◽  
Pedro Tradacete ◽  
Ignacio Villanueva
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Symmetric Tensor ◽  
Continuous Functions ◽  
Product Spaces ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions ◽  
Daugavet Property

We study the Daugavet property in tensor products of Banach spaces. We show that $L_{1}(\unicode[STIX]{x1D707})\widehat{\otimes }_{\unicode[STIX]{x1D700}}L_{1}(\unicode[STIX]{x1D708})$ has the Daugavet property when $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$ are purely non-atomic measures. Also, we show that $X\widehat{\otimes }_{\unicode[STIX]{x1D70B}}Y$ has the Daugavet property provided $X$ and $Y$ are $L_{1}$ -preduals with the Daugavet property, in particular, spaces of continuous functions with this property. With the same techniques, we also obtain consequences about roughness in projective tensor products as well as the Daugavet property of projective symmetric tensor products.

scholarly journals Banach spaces with the Daugavet property

1999 ◽  
Vol 352 (2) ◽  
pp. 855-873 ◽  
Author(s):  
Vladimir M. Kadets ◽  
Roman V. Shvidkoy ◽  
Gleb G. Sirotkin ◽  
Dirk Werner
Keyword(s):  
Banach Spaces ◽  
Daugavet Property

scholarly journals Narrow operators and rich subspaces of Banach spaces with the Daugavet property

2001 ◽  
Vol 147 (3) ◽  
pp. 269-298 ◽  
Author(s):  
Vladimir M. Kadets ◽  
Roman V. Shvidkoy ◽  
Dirk Werner
Keyword(s):  
Banach Spaces ◽  
Daugavet Property
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