À la recherche de la preuve perdue: a simple proof of the Ficken theorem

Dariusz Cichoń

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, Issue: 1, page 133-137
  • ISSN: 2300-133X

Abstract

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A new proof of the Ficken criterion is given together with a comment concerning the known proofs and related results

How to cite

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Dariusz Cichoń. "À la recherche de la preuve perdue: a simple proof of the Ficken theorem." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13.1 (2014): 133-137. <http://eudml.org/doc/268769>.

@article{DariuszCichoń2014,
abstract = {A new proof of the Ficken criterion is given together with a comment concerning the known proofs and related results},
author = {Dariusz Cichoń},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Ficken theorem},
language = {eng},
number = {1},
pages = {133-137},
title = {À la recherche de la preuve perdue: a simple proof of the Ficken theorem},
url = {http://eudml.org/doc/268769},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Dariusz Cichoń
TI - À la recherche de la preuve perdue: a simple proof of the Ficken theorem
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
IS - 1
SP - 133
EP - 137
AB - A new proof of the Ficken criterion is given together with a comment concerning the known proofs and related results
LA - eng
KW - Ficken theorem
UR - http://eudml.org/doc/268769
ER -

References

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  1. [1] D. Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications 20, Birkhäuser Verlag, Basel, 1986. Cited on 133 and 134. Zbl0617.46030
  2. [2] A.S. Besicovitch, A problem on a circle, J. London Math. Soc. 36 (1961) 241-244 Cited on 134. Zbl0097.38201
  3. [3] C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911), 193-217. Cited on 135. Zbl42.0429.01
  4. [4] A. Danelich, Normed spaces which satisfy Apollonius’ theorem, Mat. Zametki 20 (1976), 247-252. Cited on 136. 
  5. [5] M.M. Day, Normed Linear Spaces, Third edition, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag, New York-Heidelberg, 1973. Cited on 134 and 135. 
  6. [6] N. Falkner, A characterization of inner product spaces Amer. Math. Monthly 100 (1993), no. 3, 246-249. Cited on 136. Zbl0785.51010
  7. [7] F.A. Ficken, Note on the existence of scalar products in normed linear spaces, Ann. of Math. (2) 45 (1944), 362-366. Cited on 134. Zbl0060.26203
  8. [8] V.I. Istratescu, Theory and applications, Mathematics and its Applications 25, D. Reidel Publishing Co., Dordrecht, 1987. Cited on 134. 
  9. [9] E.R. Lorch, On certain implications which characterize Hilbert space, Ann. of Math. (2) 49 (1948), 523-532. Cited on 133 and 134. Zbl0031.21901

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