BEST APPROXIMATION IN NORMED LINEAR SPACES BY ELEMENTS OF LINEAR SUBSPACES

1973 ◽  
Vol 5 (2) ◽  
pp. 249-250
Author(s):  
A. L. Brown
Keyword(s):  
Best Approximation ◽  
Linear Spaces ◽  
Linear Subspaces ◽  
Normed Linear Spaces

scholarly journals Extension with larger norm and separation with double support in normed linear spaces

1980 ◽  
Vol 21 (1) ◽  
pp. 93-105 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Convex Sets ◽  
Separation Theorems ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Linear Spaces ◽  
Double Support ◽  
Linear Subspaces ◽  
Normed Linear Spaces ◽  
Whole Space

We prove, in normed linear spaces, the existence of extensions of continuous linear functionals from linear subspaces to the whole space, with arbitrarily prescribed larger norm. Also, we prove that under an additional boundedness assumption, in the known separation theorems for convex sets, there exist hyperplanes which separate and support both sets.

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