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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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.

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

First available in Project Euclid: 18 December 2018

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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.)

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


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.

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