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
Keyword(s):  
Best Approximation ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Linear Spaces ◽  
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.

scholarly journals Extensions of closed convex processes

2015 ◽  
Vol 31 (1) ◽  
pp. 31-37
Author(s):  
A. R. BAIAS ◽  
◽  
T. TRIF ◽  
Keyword(s):  
Best Approximation ◽  
Convex Cones ◽  
Linear Spaces ◽  
Convex Processes ◽  
Normed Linear Spaces

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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