On the extension of continuous linear functionals and best approximation in normed linear spaces

1965 ◽  
Vol 159 (5) ◽  
pp. 344-355 ◽  
Author(s):  
Ivan Singer
1980 ◽  
Vol 21 (1) ◽  
pp. 93-105 ◽  
Author(s):  
Ivan Singer

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.


2015 ◽  
Vol 31 (1) ◽  
pp. 31-37
Author(s):  
A. R. BAIAS ◽  
◽  
T. TRIF ◽  

In this paper we provide some norm preserving extension results for real valued closed convex processes. As a consequence, we characterize afterwards, the elements of best approximation in normed linear spaces by elements of closed convex cones using closed convex processes.


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