:57928706 I would suggest to take this into another chatroom - so that your question does not get lost among the discussion which is mainly about formatting messages in chat.
In case somebody else stumbles upon this I'll add that I the syntax is [text](url) (the same as on the main site). In this case [For which Banach spaces is the self composition operator Lipschitz?](https://mathoverflow.net/q/392231) produces: For which Banach spaces is the self composition operator Lipschitz?
And if you include a message which contains only the link to a post (and nothing else), then a bit of preview is displayed. This is called oneboxiing and works for various other things. (Comments, YouTube, Wikipedia, ...)
Let $X\subseteq \{f|f:D\rightarrow \mathbb{R}^n\}$ be a Banach space, with $C^\infty(D,\mathbb{R}^n)\subseteq X$, where $D\subseteq \mathbb{R}^n$ is open and bounded.
Let $U\subseteq X\cap \{f|f:D\rightarrow D\}$ be open, and define the operator $\Phi:U\rightarrow U$ by $\Phi(f)=f\circ f$ for all...
If $x \in \mathbb{C}^{m}$ and $A$ is a $m \times n$ matrix, prove the following inequalities: (a) $\|x\|_{\infty} \leq\|x\|_{2}$. (b) $\|x\|_{2} \leq \sqrt{m}\|x\|_{\infty}$. (c) $\mid A\left\|_{\infty} \leq \sqrt{n}\right\| A \|_{2}$. (d) $\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty}$.
How to do this last 2 inequalities I know some how I need to use (a) and (b) and use operator norm but vector product is not defined for this case
If $x \in \mathbb{C}^{m}$ and $A$ is a $m \times n$ matrix, prove the following inequalities: (a) $\|x\|_{\infty} \leq\|x\|_{2}$. (b) $\|x\|_{2} \leq \sqrt{m}\|x\|_{\infty}$. (c) $\mid A\left\|_{\infty} \leq \sqrt{n}\right\| A \|_{2}$. (d) $\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty}$. How to do this last 2 inequalities I know some how I need to use (a) and (b) and use operator norm but vector product is not defined for this case
