Subspaces of almost Daugavet spaces

Lücking, Simon

doi:10.1090/s0002-9939-2010-10722-0

Cited by 3 publications

(2 citation statements)

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“…Generalizations of T (•) were considered and studied in [12,4,5]; while relations with other parameters can be seen in [14,13,3]. Spaces X for which T (X) = 2 have been considered in [2,9,10]). In particular, a Banach space X for which T (X) = 2 must contain ℓ 1 ([2]); hence it cannot be reflexive (see also [9,Thm.…”

Section: Introduction and Basic Resultsmentioning

confidence: 99%

Thick coverings for the unit ball of a Banach space

Castillo,

Papini,

Simoes

2013

Preprint

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Section: Introduction and Basic Resultsmentioning

confidence: 99%

Thick coverings for the unit ball of a Banach space

Castillo,

Papini,

Simoes

2013

Preprint

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“…Most of what is known concerning T (X) and t(X) can be found by combining [22], [5] and [8] (note that the two latter overlap a bit on T -results). The particular case when X is separable and T (X) = 2 is thoroughly described in terms of the almost Daugavet property in [17] and [19]. For the non-separable case see [14].…”

Section: Introductionmentioning

confidence: 99%

On thickness and thinness of Banach spaces

Abrahamsen,

Langemets,

Lima

et al. 2014

Preprint

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The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming ℓp-sums of Banach spaces, and obtain formulas which show that they behave rather differently. Secondly, we consider the relation of the indices of the space and a subspace. Finally, every Banach space X containing a copy of c0 can be equivalently renormed so that in the new norm c0 is an M-ideal in X and both the thickness and thinness index of X equal 1.2010 Mathematics Subject Classification. 46B20; 46B03.

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Stability of average roughness, octahedrality, and strong diameter $2$ properties of Banach spaces with respect to absolute sums

Haller¹,

Langemets²,

Nadel³

2018

Banach J. Math. Anal.

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We prove that, if Banach spaces X and Y are δaverage rough, then their direct sum with respect to an absolute norm N is δ/N (1, 1)-average rough. In particular, for octahedral X and Y and for p in (1, ∞) the space X ⊕ p Y is 2 1−1/p -average rough, which is in general optimal. Another consequence is that for any δ in (1, 2] there is a Banach space which is exactly δ-average rough. We give a complete characterization when an absolute sum of two Banach spaces is octahedral or has the strong diameter 2 property. However, among all of the absolute sums, the diametral strong diameter 2 property is stable only for 1-and ∞-sums.2010 Mathematics Subject Classification. Primary 46B20, 46B22.

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Subspaces of almost Daugavet spaces

Cited by 3 publications

References 4 publications

Thick coverings for the unit ball of a Banach space

Thick coverings for the unit ball of a Banach space

On thickness and thinness of Banach spaces

Stability of average roughness, octahedrality, and strong diameter $2$ properties of Banach spaces with respect to absolute sums

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