On inner product spaces - III

• Autorzy: Kannapann P.
• Języki publikacji: EN

Abstrakty

EN

When one deals with normed linear space (n.l.s.), the natural question arises when a n.l.s. is an inner product space (i.p.s.)? What further conditions the norm has to satisfy so that the n.l.s. an inner product space? Numerous charakterizations are known [2, 1, 2, 4, 5, 6, 7]. In this paper we study i.p.s. from functional equations point of view and consider three functional equations (ME), (14) and (15) which are generalizations of (LE) found in [6].

Słowa kluczowe

EN

additive function; inner product space; Jordan-von Neuman identity; quadratic functional equation

PL

analiza funkcjonalna; funkcja addytywna; równanie funkcjonalne kwadratowe; tożsamość Jordana-von Neumana

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no 1
• Strony: 1--4
• Opis fizyczny: Bibliogr. 7 poz.,

Twórcy

autor

Kannapann P.

• Department of Pure Mathematics, University of Waterloo, Waterloo ON, N21 3G1 Canada

Bibliografia

• [1] J. Aczél, J. Dhombres , Funnctional equations in several variabls, Сambridge Universit,y Press, Cambridge 1989.
• [2] D. Amir, Сharacterіzations of inner product spaces, Birkhauser Verlag, Base1 1986.
• [3] М. М. Day, Some characterizations of inner-product spaces, Trans. Amer. Math. Soc., 62 (1947) 320-327.
• [4] М. М. Day, On certain criteria of Кasahаra and Blumenthal for inner-product spaces, Proc. Amer. Math. Soc.. 10 (1959) 92-100.
• [5] P. Jordаn., J. von Neumann, On inne-r prпducts in linia-r inetrie spaces, Ann. Maths., 36 (1935) 719-723.
• [6] E. R. Lorch. On certain implications which characterize Hilbert space, Ann. Maths., 49 (1948) 523--532.
• [7] J.J. Schoenberg, A remark on M. M. Daу's characterizations of Hilbert spaсs, Proc. Amer. Math. Soc., 3 (1952) 961-964.