scholarly journals Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

2016 ◽  
Vol 20 (1) ◽  
pp. 101
Author(s):  
Rainis Haller ◽  
Katriin Pirk ◽  
Märt Põldvere
Keyword(s):  
Banach Spaces ◽  
Direct Sums ◽  
Diameter Two Property

Countable Direct Sums of Banach Spaces

1989 ◽  
Vol 141 (1) ◽  
pp. 73-79
Author(s):  
M. Valdivia
Keyword(s):  
Banach Spaces ◽  
Direct Sums

scholarly journals Deviation from weak Banach–Saks property for countable direct sums

2014 ◽  
Vol 68 (2) ◽  
Author(s):  
Andrzej Kryczka
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Direct Sums ◽  
Bounded Linear

AbstractWe introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (X

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.

Strict convexity of absolute norms on and direct sums of banach spaces

2002 ◽  
Vol 2002 (2) ◽  
pp. 209507 ◽  
Author(s):  
Yasuji Takahashi ◽  
Mikio Kato ◽  
Kichi-Suke Saito
Keyword(s):  
Banach Spaces ◽  
Strict Convexity ◽  
Direct Sums

Multiplicity of direct sums of operators on Banach spaces

2009 ◽  
Vol 41 (6) ◽  
pp. 1041-1052
Author(s):  
Sophie Grivaux ◽  
Maria Roginskaya
Keyword(s):  
Banach Spaces ◽  
Direct Sums

scholarly journals Proximinality in generalized direct sums

2004 ◽  
Vol 2004 (67) ◽  
pp. 3663-3670
Author(s):  
Darapaneni Narayana ◽  
T. S. S. R. K. Rao
Keyword(s):  
Banach Spaces ◽  
Finite Codimension ◽  
Direct Sums

We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.

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