On characterizations of inner-product spaces.
Kapoor, O.P., Prasad, Jagadish (1984)
Publications de l'Institut Mathématique. Nouvelle Série
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Displaying similar documents to “On isomorphisms by orthogonality of a normed space and an inner product space.”
On characterizations of inner-product spaces.
Characterizations of inner product spaces through an isosceles trapezoid property
Claudi Alsina, P. Cruells, M. S. Tomás (1999)
Archivum Mathematicum
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Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference
Claudi Alsina, Piedad Guijarro Carranza, M. S. Tomás (1996)
Archivum Mathematicum
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We define the radius of the inscribed and circumscribed circumferences in a triangle located in a real normed space and we obtain new characterizations of inner product spaces.
On (a,b,c,d)-orthogonality in normed linear spaces
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.
Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
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...