×
Banakh, Taras; Garbulińska-Węgrzyn, Joanna

The universal Banach space with a \(K\)-suppression unconditional basis. (English) Zbl 1463.46017

Commentat. Math. Univ. Carol. 59, No. 2, 195-206 (2018); corrigendum ibid. 61, No. 1, 127-128 (2020).
Summary: Using the technique of Fraïssé theory, for every constant \(K\geq 1\), we construct a universal object \(\mathbb{U}_K\) in the class of Banach spaces possessing a normalized \(K\)-suppression unconditional Schauder basis.

Cited in 1 Review
Cited in 1 Document

MSC:

46B04 Isometric theory of Banach spaces
46M15 Categories, functors in functional analysis
46M40 Inductive and projective limits in functional analysis

Keywords:

\(1\)-suppression unconditional Schauder basis; rational spaces; isometry
PDF BibTeX XML Cite
\textit{T. Banakh} and \textit{J. Garbulińska-Węgrzyn}, Commentat. Math. Univ. Carol. 59, No. 2, 195--206 (2018; Zbl 1463.46017)
Full Text: DOI arXiv
  • logo of hbz
  • logo of WorldCat

References:

[1] Albiac F.; Kalton N. J., Topics in Banach Space Theory, Graduate Texts in Mathematics, 233, Springer, Cham, 2016 · Zbl 1094.46002
[2] Fabián M.; Halaba P.; Hájek P.; Montesinos Santalucía V.; Pelant J.; Zízler V., Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 8, Springer, New York, 2001
[3] Fraïssé R., Sur quelques classifications des systèmes de relations, Publ. Sci. Univ. Alger. Sér. A. 1 (1954), 35-182 (French)
[4] Garbulińska-Wegrzyn J., Isometric uniqueness of a complementably universal Banach space for Schauder decompositions, Banach J. Math. Anal. 8 (2014), no. 1, 211-220 · Zbl 1286.46012
[5] Gurariĭ V. I., Spaces of universal placement, isotropic spaces and a problem of Mazur on rotations of Banach spaces, Sibirsk. Mat. Zh. 7 (1966), 1002-1013 (Russian) · Zbl 0166.39303
[6] Johnson W. B.; Szankowski A., Complementably universal Banach spaces, Studia Math. 58 (1976), no. 1, 91-97 · Zbl 0341.46017
[7] Kadec’ M. Ĭ., On complementably universal Banach spaces, Studia Math. 40 (1971), 85-89 · Zbl 0218.46015
[8] Kubiś W., Fraïssé sequences: category-theoretic approch to universal homogeneous structures, Ann. Pure Appl. Logic 165 (2014), no. 11, 1755-1811 · Zbl 1329.18002
[9] Kubiś W.; Solecki S., A proof of uniqueness of the Gurariĭ space, Israel J. Math. 195 (2013), no. 1, 449-456 · Zbl 1290.46010
[10] Pełczyński A., Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228 · Zbl 0104.08503
[11] Pełczyński A., Universal bases, Studia Math. 32 (1969), 247-268 · Zbl 0185.37401
[12] Pełczyński A., Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-243 · Zbl 0223.46019
[13] Pełczyński A.; Wojtaszczyk P., Banach spaces with finite-dimensional expansions of identity and universal bases of finite-dimensional subspaces, Studia Math. 40 (1971), 91-108 · Zbl 0221.46014
[14] Schechtman G., On Pełczyński’s paper “Universal bases” (Studia Math. 32 (1969), 247-268), Israel J. Math. 22 (1975), no. 3-4, 181-184
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.