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December 2018 On the separable quotient problem for Banach spaces
Juan C. Ferrando, Jerzy Kąkol, Manuel López-Pellicer, Wiesław Śliwa
Funct. Approx. Comment. Math. 59(2): 153-173 (December 2018). DOI: 10.7169/facm/1704

Abstract

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of infinite-dimensional separable quotients in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the presented results are consequences of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces $c_{0}$ and $\ell _{p}$, for $1\leq p\leq \infty $. Also recent results of Argyros, Dodos, Kanellopoulos [1] and Śliwa [64] are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica.

Citation

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Juan C. Ferrando. Jerzy Kąkol. Manuel López-Pellicer. Wiesław Śliwa. "On the separable quotient problem for Banach spaces." Funct. Approx. Comment. Math. 59 (2) 153 - 173, December 2018. https://doi.org/10.7169/facm/1704

Information

Published: December 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07055550
MathSciNet: MR3892305
Digital Object Identifier: 10.7169/facm/1704

Subjects:
Primary: 30H20
Secondary: 46B28, 46E27, 46E30

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.59 • No. 2 • December 2018
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