The equation x^2-I=0 has infinitely many solutions on L(R).
Prove.
What is $\displaystyle L(R)$? What do you mean by $\displaystyle x^2-I$? The first thing that comes to mind is $\displaystyle L^1(\mathbb{R} )$ and $\displaystyle x$ an operator $\displaystyle x:L^1(\mathbb{R} ) \rightarrow L^1 (\mathbb{R} )$. Am I right? Please give all the relevant definitions.