Some remarks on inequalities that characterize inner product spaces.
Alonso, Javier (1992)
International Journal of Mathematics and Mathematical Sciences
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Alonso, Javier (1992)
International Journal of Mathematics and Mathematical Sciences
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Carlos Benítez Rodríguez (1989)
Revista Matemática de la Universidad Complutense de Madrid
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Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized...
Javier Alonso, Carlos Benítez (1989)
Extracta Mathematicae
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F. Javier Alonso Romero, Carlos Benítez Rodríguez (1986)
Extracta Mathematicae
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Javier Alonso, Carlos Benítez (1988)
Extracta Mathematicae
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C.-S. Lin (2005)
Colloquium Mathematicae
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We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.
Carlos Benítez, Krzysztof Przesławski, David Yost (1998)
Studia Mathematica
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We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.
María D. Acosta (1995)
Extracta Mathematicae
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Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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