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A counterexample to the approximation problem in Banach spaces. (English) Zbl 0267.46012


MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46B99 Normed linear spaces and Banach spaces; Banach lattices
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References:

[1] Grothendieck, A., Produits tensoriels topologiques et espaces nucleaires.Mem. Amer. Math. Soc., 16 (1955). · Zbl 0123.30301
[2] Enflo, P., A Banach space with basis constant >1.Arkiv för matematik, 11 (1973), 103–107. · Zbl 0267.46011 · doi:10.1007/BF02388509
[3] Johnson, W. B., Rosenthal, H. P., &Zippin, M., On bases, finite-dimensional decompositions and weaker structures in Banach spaces.Israel J. Math. 9 (1971), 488–506. · Zbl 0217.16103 · doi:10.1007/BF02771464
[4] Johnson, W. B., A complementably universal conjugate Banach space and its relation to the approximation problem.Israel J. Math. 13 (1972), 301–310. · doi:10.1007/BF02762804
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