Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Inner products in normed linear spaces


Author: Robert C. James
Journal: Bull. Amer. Math. Soc. 53 (1947), 559-566
DOI: https://doi.org/10.1090/S0002-9904-1947-08831-5
MathSciNet review: 0021242
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. S. Banach, Théorie des operations linéaires, Warsaw, 1932.
  • 2. Garrett Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), no. 2, 169–172. MR 1545873, https://doi.org/10.1215/S0012-7094-35-00115-6
  • 3. R. Fortet, Remarques sur les espaces uniformément convexes, Bull. Soc. Math. France vol. 69 (1941) pp. 23-46. MR 13225
  • 4. R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 265-292. MR 21241
  • 5. P. Jordan and J. Von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719–723. MR 1503247, https://doi.org/10.2307/1968653
  • 6. S. Kakutani, Some characterizations of Euclidean space, Jap. J. Math. vol. 16 (1939) pp. 93-97. MR 895
  • 7. H. Löwig, Komplexe Euklidische Räume von beliebiger endlicher oder transfiniter Dimensionszahl, Acta Litterarum ac Scientiarum vol. 7 (1934-1935) pp. 1-33.
  • 8. S. Mazur, Über convexe Mengen in linearen normierten Räumen, Studia Mathematica vol. 4 (1933) pp. 70-84.
  • 9. V. Šmulian, On some geometrical properties of the unit sphere in the space of the type (B), Rec. Math. (Mat. Sbornik) N.S. vol. 48 (1938) pp. 90-94.
  • 10. Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1947-08831-5

American Mathematical Society