Functiones et Approximatio Commentarii Mathematici

On the separable quotient problem for Banach spaces

Juan C. Ferrando, Jerzy Kąkol, Manuel López-Pellicer, and Wiesław Śliwa

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 153-173.

Dates
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1545102409

Digital Object Identifier
doi:10.7169/facm/1704

Mathematical Reviews number (MathSciNet)
MR3892305

Subjects
Primary: 30H20: Bergman spaces, Fock spaces
Secondary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46E27: Spaces of measures [See also 28A33, 46Gxx] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Banach space barrelled space separable quotient vector-valued function space linear operator space vector measure space tensor product Radon-Nikodým property

Citation

Ferrando, Juan C.; Kąkol, Jerzy; López-Pellicer, Manuel; Śliwa, Wiesław. On the separable quotient problem for Banach spaces. Funct. Approx. Comment. Math. 59 (2018), no. 2, 153--173. doi:10.7169/facm/1704. https://projecteuclid.org/euclid.facm/1545102409


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