Schauder basis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Schauder basis" in English language version.

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See James (1950) and Lindenstrauss & Tzafriri (1977, p. 9). James, Robert C. (1950). "Bases and reflexivity of Banach spaces". The Annals of Mathematics. 52 (3): 518–527. doi:10.2307/1969430. MR 39915 Lindenstrauss, Joram; Tzafriri, Lior (1977), Classical Banach Spaces I, Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92, Berlin: Springer-Verlag, ISBN 3-540-08072-4
See James (1950) and Lindenstrauss & Tzafriri (1977, p. 23). James, Robert C. (1950). "Bases and reflexivity of Banach spaces". The Annals of Mathematics. 52 (3): 518–527. doi:10.2307/1969430. MR 39915 Lindenstrauss, Joram; Tzafriri, Lior (1977), Classical Banach Spaces I, Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92, Berlin: Springer-Verlag, ISBN 3-540-08072-4

amu.edu.pl

kielich.amu.edu.pl

see Bočkarev, S. V. (1974), "Existence of a basis in the space of functions analytic in the disc, and some properties of Franklin's system", (in Russian) Mat. Sb. (N.S.) 95(137): 3–18, 159. Translated in Math. USSR-Sb. 24 (1974), 1–16. The question is in Banach's book, Banach (1932) p. 238, §3. Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.
see p. 238, §3 in Banach (1932). Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.

arxiv.org

Gowers, W. Timothy; Maurey, Bernard (6 May 1992). "The unconditional basic sequence problem". arXiv:math/9205204.

doi.org

see Schauder (1927). Schauder, Juliusz (1927), "Zur Theorie stetiger Abbildungen in Funktionalraumen", Mathematische Zeitschrift (in German), 26: 47–65, doi:10.1007/BF01475440, hdl:10338.dmlcz/104881.
Schauder, Juliusz (1928). "Eine Eigenschaft des Haarschen Orthogonalsystems". Mathematische Zeitschrift. 28: 317–320. doi:10.1007/bf01181164.
Karlin, S. (December 1948). "Bases in Banach spaces". Duke Mathematical Journal. 15 (4): 971–985. doi:10.1215/S0012-7094-48-01587-7. ISSN 0012-7094.
Enflo, Per (July 1973). "A counterexample to the approximation problem in Banach spaces". Acta Mathematica. 130 (1): 309–317. doi:10.1007/BF02392270.
see pp. 48–49 in Schauder (1927). Schauder defines there a general model for this system, of which the Faber–Schauder system used today is a special case. Schauder, Juliusz (1927), "Zur Theorie stetiger Abbildungen in Funktionalraumen", Mathematische Zeitschrift (in German), 26: 47–65, doi:10.1007/BF01475440, hdl:10338.dmlcz/104881.
Franklin, Philip (1928). "A set of continuous orthogonal functions". Math. Ann. 100: 522–529. doi:10.1007/bf01448860.
see Ciesielski, Z (1969). "A construction of basis in C¹(I²)". Studia Math. 33: 243–247. and Schonefeld, Steven (1969). "Schauder bases in spaces of differentiable functions". Bull. Amer. Math. Soc. 75 (3): 586–590. doi:10.1090/s0002-9904-1969-12249-4.
see Szankowski, Andrzej (1981). "B(H) does not have the approximation property". Acta Math. 147: 89–108. doi:10.1007/bf02392870.
See James (1950) and Lindenstrauss & Tzafriri (1977, p. 9). James, Robert C. (1950). "Bases and reflexivity of Banach spaces". The Annals of Mathematics. 52 (3): 518–527. doi:10.2307/1969430. MR 39915 Lindenstrauss, Joram; Tzafriri, Lior (1977), Classical Banach Spaces I, Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92, Berlin: Springer-Verlag, ISBN 3-540-08072-4
See James (1950) and Lindenstrauss & Tzafriri (1977, p. 23). James, Robert C. (1950). "Bases and reflexivity of Banach spaces". The Annals of Mathematics. 52 (3): 518–527. doi:10.2307/1969430. MR 39915 Lindenstrauss, Joram; Tzafriri, Lior (1977), Classical Banach Spaces I, Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92, Berlin: Springer-Verlag, ISBN 3-540-08072-4

handle.net

hdl.handle.net

see Schauder (1927). Schauder, Juliusz (1927), "Zur Theorie stetiger Abbildungen in Funktionalraumen", Mathematische Zeitschrift (in German), 26: 47–65, doi:10.1007/BF01475440, hdl:10338.dmlcz/104881.
see pp. 48–49 in Schauder (1927). Schauder defines there a general model for this system, of which the Faber–Schauder system used today is a special case. Schauder, Juliusz (1927), "Zur Theorie stetiger Abbildungen in Funktionalraumen", Mathematische Zeitschrift (in German), 26: 47–65, doi:10.1007/BF01475440, hdl:10338.dmlcz/104881.

projecteuclid.org

Karlin, S. (December 1948). "Bases in Banach spaces". Duke Mathematical Journal. 15 (4): 971–985. doi:10.1215/S0012-7094-48-01587-7. ISSN 0012-7094.

uni-goettingen.de

www-gdz.sub.uni-goettingen.de

Faber, Georg (1910), "Über die Orthogonalfunktionen des Herrn Haar", Deutsche Math.-Ver (in German) 19: 104–112. ISSN 0012-0456; http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN37721857X ; http://resolver.sub.uni-goettingen.de/purl?GDZPPN002122553

resolver.sub.uni-goettingen.de

Faber, Georg (1910), "Über die Orthogonalfunktionen des Herrn Haar", Deutsche Math.-Ver (in German) 19: 104–112. ISSN 0012-0456; http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN37721857X ; http://resolver.sub.uni-goettingen.de/purl?GDZPPN002122553

web.archive.org

see Bočkarev, S. V. (1974), "Existence of a basis in the space of functions analytic in the disc, and some properties of Franklin's system", (in Russian) Mat. Sb. (N.S.) 95(137): 3–18, 159. Translated in Math. USSR-Sb. 24 (1974), 1–16. The question is in Banach's book, Banach (1932) p. 238, §3. Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.
see p. 238, §3 in Banach (1932). Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.

worldcat.org

Faber, Georg (1910), "Über die Orthogonalfunktionen des Herrn Haar", Deutsche Math.-Ver (in German) 19: 104–112. ISSN 0012-0456; http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN37721857X ; http://resolver.sub.uni-goettingen.de/purl?GDZPPN002122553
Karlin, S. (December 1948). "Bases in Banach spaces". Duke Mathematical Journal. 15 (4): 971–985. doi:10.1215/S0012-7094-48-01587-7. ISSN 0012-7094.

zbmath.org

see Bočkarev, S. V. (1974), "Existence of a basis in the space of functions analytic in the disc, and some properties of Franklin's system", (in Russian) Mat. Sb. (N.S.) 95(137): 3–18, 159. Translated in Math. USSR-Sb. 24 (1974), 1–16. The question is in Banach's book, Banach (1932) p. 238, §3. Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.
see p. 238, §3 in Banach (1932). Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020.