Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a complete probability space. Since $L^2(\Omega,\mathcal{F},\mathbb{P})$ is a subspace of $L^1(\Omega,\mathcal{F},\mathbb{P})$, is there a well-defined/studied projection operator from $L^1(\Omega,\mathcal{F},\mathbb{P})$ onto $L^2(\Omega,\mathcal{F},\mathbb{P})$?
If so, could someone provide a reference/ let me know why this topic is not commonly studied?