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Proceedings of the American Mathematical Society

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On the norm of the product
of linear functionals


Authors: C. Benítez, Manuel Fernández and María L. Soriano
Journal: Proc. Amer. Math. Soc. 127 (1999), 1437-1441
MSC (1991): Primary 46C15, 46B20
DOI: https://doi.org/10.1090/S0002-9939-99-04997-7
Published electronically: January 29, 1999
MathSciNet review: 1622777
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Abstract | References | Similar Articles | Additional Information

Abstract: Real inner product spaces are characterized by the points at which the homogeneous 2-polynomials that are products of equal-norm linear functionals attain their norm.


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

  • 1. Dan Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications, vol. 20, Birkhäuser Verlag, Basel, 1986. MR 897527
  • 2. Marco Baronti, On some parameters of normed spaces, Boll. Un. Mat. Ital. B (5) 18 (1981), no. 3, 1065–1085 (Italian, with English summary). MR 641756
  • 3. M.M. DAY, Some characterizations of inner product spaces, Trans. Amer. Math. Soc., 62 (1947), 320-337. MR 9:192c
  • 4. R.C. JAMES, Inner products in normed linear spaces, Bull. Amer. Math. Soc., 53 (1947), 559-566. MR 9:42d

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Additional Information

C. Benítez
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
Email: cabero@unex.es

Manuel Fernández
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

María L. Soriano
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

DOI: https://doi.org/10.1090/S0002-9939-99-04997-7
Keywords: Characterization of inner product spaces
Received by editor(s): August 24, 1997
Published electronically: January 29, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society