wayneckm
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Hello all,
My question is if [tex]f : X \mapsto Y[/tex] is an isometry which preserves norm, i.e. [tex]\left\| f(x) \right\| _{Y} = \left\| x \right\|_{X}[/tex], does this imply [tex]\left\| f(x_2) - f(x_1) \right\| _{Y} = \left\| x_2 - x_1 \right\|_{X}[/tex]?
Or, essentially is it sufficient to gurantee convergence in [tex]X[/tex]-norm implies convergence in [tex]Y[/tex]-norm under the map [tex]f[/tex]?
Thanks a lot.
Wayne
My question is if [tex]f : X \mapsto Y[/tex] is an isometry which preserves norm, i.e. [tex]\left\| f(x) \right\| _{Y} = \left\| x \right\|_{X}[/tex], does this imply [tex]\left\| f(x_2) - f(x_1) \right\| _{Y} = \left\| x_2 - x_1 \right\|_{X}[/tex]?
Or, essentially is it sufficient to gurantee convergence in [tex]X[/tex]-norm implies convergence in [tex]Y[/tex]-norm under the map [tex]f[/tex]?
Thanks a lot.
Wayne