Abstract
Let \(X,Y\) be two normed spaces, \(X_{1}\) a subspace of \(X\) and \(A:X\rightarrowY\) a continuous linear operator. Let us denote \(Z_{1}=Ker\left( \left. A\right \vert _{X_{1}}\right) ,Z=KerA\) and for \(x\in X,E\left( x\right)=\{y\in X:Ax=Ay\) and \(\left \Vert y\right \Vert =\left \Vert Ax\right \Vert/\left \Vert A\right \Vert \}\) and \(E_{1}\left( x\right) =\{y_{1}\in X_{1}:Ax=Ay_{1}\) and \(\left \Vert y_{1}\right \Vert =\left \Vert Ax\right \Vert/\left \Vert A\right \Vert \}\). One gives the relations between the sets \(E\left( x\right)\), \(E_{1}\left(x\right)\) and \(P_{Z}\left( x\right)\), \(P_{Z_{1}}\left( x\right)\) where \(P_{C}\left( x\right) :\{y\in C:\left \Vert x-y\right \Vert =d\left(x,C\right) \}\). An application is considered.
Authors
Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
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Paper coordinates
C. Mustăţa, Some remarks concerning norm preserving extension and best approximation, Rev. Anal. Numer. Theor. Approx., 29 (2000) No. 2, pp. 173-180.
About this paper
Journal
Revue d’Analyse Numer.Theor. Approx.
Publisher Name
Publishing Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
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