×
Tapia, R. A.

A characterization of inner product spaces. (English) Zbl 0286.46025

Proc. Am. Math. Soc. 41, 569-574 (1973).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0286.46025

Cited in 6 Reviews
Cited in 8 Documents

MSC:

46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46B99 Normed linear spaces and Banach spaces; Banach lattices
Cite Review PDF
Full Text: DOI

References:

[1] Jean-Pierre Aubin, Optimal approximation and characterization of the error and stability functions in Banach spaces, J. Approximation Theory 3 (1970), 430 – 444. · Zbl 0222.46011
[2] Arne Beurling and A. E. Livingston, A theorem on duality mappings in Banach spaces, Ark. Mat. 4 (1962), 405 – 411 (1962). · Zbl 0105.09301 · doi:10.1007/BF02591622
[3] Robert Bonic and Flavio Reis, A characterization of Hilbert space, An. Acad. Brasil. Ci. 38 (1966), 239 – 241. · Zbl 0185.20004
[4] Dennis F. Cudia, The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284 – 314. · Zbl 0123.30701
[5] M. Golomb and R. A. Tapia, The metric gradient in normed linear spaces, Numer. Math. 20 (1972/73), 115 – 124. · Zbl 0277.65037 · doi:10.1007/BF01404401
[6] V. L. Klee Jr., Some characterizations of reflexivity, Revista Ci., Lima 52 (1950), no. nos. 3-4, 15 – 23. · Zbl 0040.35403
[7] Josef Kolomý, Some remarks on nonlinear functionals, Comment. Math. Univ. Carolinae 11 (1970), 693 – 704. · Zbl 0205.43303
[8] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29 – 43. · Zbl 0102.32701
[9] S. Mazur, Über konvexe Mengen in linearen normierten Raumen, Studia Math. 4 (1933), 70-84. · JFM 59.1074.01
[10] Robert M. McLeod, Mean value theorems for vector valued functions, Proc. Edinburgh Math. Soc. (2) 14 (1964/1965), 197 – 209. · Zbl 0135.34301 · doi:10.1017/S0013091500008786
[11] Kondagunta Sundaresan, Smooth Banach spaces, Math. Ann. 173 (1967), 191 – 199. · Zbl 0158.13701 · doi:10.1007/BF01361710
[12] R. A. Tapia, A characterization of inner product spaces, Bull. Amer. Math. Soc. 79 (1973), 530 – 531. · Zbl 0271.46014
[13] M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1964. With a chapter on Newton’s method by L. V. Kantorovich and G. P. Akilov. Translated and supplemented by Amiel Feinstein.
[14] E. H. Zarantonello, The meaning of the Cauchy-Schwarz-Buniakovsky inequality, Mathematics Research Center Report 1277, University of Wisconsin, Madison, Wis., 1972. · Zbl 0348.47037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.