# Reference Request: Projection from $L^1$ onto $L^2$

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?

• Certainly not a continuous one, because $L^2(\Omega,\mathcal F,\Bbb P)$ (as a subspace) is dense in $L^1(\Omega,\mathcal F,\Bbb P)$. – Saucy O'Path Apr 1 at 10:50
• Indeed, but is there some studied notion? – AIM_BLB Apr 1 at 11:00