- #1

- 58

- 0

## Homework Statement

Show that

[tex]\frac{\Vert X(u+v) \Vert}{\Vert u+v \Vert} \leq \max \{

\frac{\Vert Xu \Vert}{\Vert u \Vert}, \frac{\Vert Xv \Vert}{\Vert v \Vert} \}

[/tex]

## Homework Equations

## The Attempt at a Solution

Tried to rewrite the max statement as an inequality (without loss of genreality). Then However I can't really get anyway with it since

when I try to estimate the numerator or the denominator independently (triangle inequality, ...) I get a bound which is too high and I don't really know how to estimate both simultaniuously.

thx