# Thread: A family of operators with a specific property

1. ## A family of operators with a specific property

Hi! I'm stuck trying to solve the below stated problem. (Any suggestions and help is more than welcome). Thanks!

PROBLEM: Define $T_b$ by $T_b f(t)=bf(t)$ (where $f(t)\in L^p([0,1])$ and $1\leq p$ fixed). The task is to find all bounded linear maps $T$ from $L^p([0,1])$ to $L^p([0,1])$ with the property $TT_b=T_bT$.

2. ## Re: A family of operators with a specific property

Is $b$ a function?

3. ## Re: A family of operators with a specific property

No, b is just an independent variable.