Caracterización de aproximaciones óptimas en espacios producto.
Una propiedad de la ortogonalidad de Birkhoff y una caracterización de espacios prehilbertianos.
Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
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 concepts...
Norms in product spaces which preserve approximation properties.
Functional characterization of best and good approximation in normed product spaces.
In [6], C. Dierick deals with a small but important collection of norms in the product of a finite number of normed linear spaces and he extends to such products some results on functional characterization of best approximations. In this paper we establish the widest scope in which the mentioned results remain valid.
Orthogonality in normed linear spaces: A survey. Part II: Relations between main orthogonalities.
Orthogonality in normed linear spaces. A survey I: Main properties.
A universal modulus for normed spaces
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.
The Joly's construction: A common property of some generalized orthogonalities.
Suitable norms for simultaneous approximation.
Some characteristic and non-characteristic properties of inner product spaces
Location of the 2-centers of three points.
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