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
?
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