Prove that: if  $g \in L^{\infty}$, the operator $T$ defined by $Tf = fg$ is bounded on $L^{p}$ for $1\leq p\leq \infty$. Its operator norm is at most $||g||_{\infty}$, with equality if $\mu$ is semifinite, where $\mu$ is the measure on $\mathcal{M}$, the measure space.

My approach: I consider $\hat{g(x)}(f) = f(g(x))$, which is a linear operator on $L^{p}$. Clearly $||\hat{g(x)}||  = ||g(x) || \leq ||g||_{\infty}$ , which gives me the first part of the proof. I am clueless about the second part, involving semifinite measure. 


Question: Why don't banks give access to all your transaction activity?
Answer: If you need access to your data beyond the online availability, you download the transactions and manage the archive yourself. Six months to eighteen months is generally enough time for most people to manage their own archived data.

Big banks have the power to store and retrieve all the data online. Unfortunately, the older records are not frequently accessed. Why have these records online when they will be rarely accessed? Backing up data will take longer. Queries to retrieve data will take longer. Everything will take longer just so you can have records that 99% of customers will never access.