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By using the concepts of limited $p$ -converging operators between two Banach spaces $X$ and $Y$ , $L_{p}$ -sets and $L_{p}$ -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as $*$ -Dunford–Pettis property of order $p$ and Pelczyński’s property of order $p$ , $1 \leq p < \infty$ .

Lipschitz and uniform embeddings into $ℓ_{\infty}$

N. J. Kalton (2011)

Fundamenta Mathematicae

We show that there is no uniformly continuous selection of the quotient map $Q : ℓ_{\infty} \to ℓ_{\infty} / c ₀$ relative to the unit ball. We use this to construct an answer to a problem of Benyamini and Lindenstrauss; there is a Banach space X such that there is a no Lipschitz retraction of X** onto X; in fact there is no uniformly continuous retraction from $B_{X * *}$ onto $B_{X}$ .

Locally uniformly non- $l_{n}^{(1)}$ Orlicz spaces

Hudzik, H. (1985)

Proceedings of the 13th Winter School on Abstract Analysis

L-sets and the Pelczynski-Pitt theorem.

Jesús M. Fernández Castillo, Ricardo García (2005)

Extracta Mathematicae

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