Let $A$ be a square Matrix and $||\cdot ||\_p$ the induced Matrix norm for $1 \leq p \leq \infty$. Is it true that
$$||A||\_p\leq \max(||A||\_1,||A||\_{\infty})?$$
For $p=2$ the answer is yes because $||A||\_2^2\leq ||A||\_1||A||\_{\infty}$.


The motivation is that I have a family of matrices where I can bound the infinity and 1-Norm but I dont know how to bound the $p$-Norm.


Thx for any help in advance



Matrix-Norm equivalence with p-Norm
Yes, by the [Riesz-Thorin theorem](https://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theorem).


