Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces of Finite Dimension

  • Ivan Singer
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 171)


An important particular case of best approximation in normed linear spaces E by elements of linear subspaces G is that when the dimension (real or complex, according to the space E) of G is finite: dim G = n < ∞. In this case*) G = [x 1,..., x n], where x 1,..., x n are linearly independent elements of G, and every element gG can be written, uniquely, in the form
$$g = \sum\limits_{k = 1}^n {\alpha _k x_k } $$
where α1,..., α n are scalars (real or complex, according to the space E); the linear combinations (1.1) are also called polynomials (in x 1,..., x n ).


Banach Space Extremal Point Linear Subspace Compact Space Finite Dimension 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Ivan Singer
    • 1
  1. 1.Institute of MathematicsAcademy of the Socialist Republic of RomaniaBucharestRomania

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