A family of operators with a specific property

**kenza** · January 15th 2012, 03:15 PM

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 $TT_b=T_bT$ .

**girdav** · January 16th 2012, 12:02 PM

Is $b$ a function?

**kenza** · January 16th 2012, 01:22 PM

No, b is just an independent variable.

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