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

• Autorzy: Dariusz Cichoń
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
• Czasopismo: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
• Rocznik: 2014
• Tom: 13

Daty

wydano

2014-12-01

otrzymano

2014-05-22

poprawiono

2014-09-24

online

2014-12-11

Twórcy

autor

Dariusz Cichoń

• Faculty of Mathematics and Computer Science Jagiellonian University Łojasiewicza 6, PL-30-348 Kraków Poland

Bibliografia

• [1] D. Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications 20, Birkhäuser Verlag, Basel, 1986. Cited on 133 and 134.
• [2] A.S. Besicovitch, A problem on a circle, J. London Math. Soc. 36 (1961) 241-244 Cited on 134.
• [3] C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911), 193-217. Cited on 135.
• [4] A. Danelich, Normed spaces which satisfy Apollonius’ theorem, Mat. Zametki 20 (1976), 247-252. Cited on 136.
• [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] N. Falkner, A characterization of inner product spaces Amer. Math. Monthly 100 (1993), no. 3, 246-249. Cited on 136.
• [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.
• [8] V.I. Istratescu, Theory and applications, Mathematics and its Applications 25, D. Reidel Publishing Co., Dordrecht, 1987. Cited on 134.
• [9] E.R. Lorch, On certain implications which characterize Hilbert space, Ann. of Math. (2) 49 (1948), 523-532. Cited on 133 and 134.

Identyfikatory

DOI

10.2478/aupcsm-2014-0010