1
$\begingroup$

Let V be a vector space over $\mathbb{R}$ or $\mathbb{C}$. Let (V, ||·||) be a normed space.
Let $x,y\in V$, then $||x||\leq \max{\{||x+y||, ||x-y||\}}$
This may seem trivial but I am stuck with it.
I have tried with both triangle and reverse triangle inequality. But it only gets to this, $||x||\leq ||x-y|| + ||y||$ or $||x||\leq ||x||+||y||$.

$\endgroup$
1
  • 3
    $\begingroup$ stuck where? show what you have tried! $\endgroup$
    – mark
    Oct 19, 2021 at 9:14

1 Answer 1

2
$\begingroup$

Here is a hint: $$ 2\|x\|=\|(x+y)+(x-y)\|. $$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .