## Operator on Hilbert space

$(H, \langle .,. \rangle)$ Hilbert space, and $f_1$, $f_2$ $\in H$.
Prove: $Af= \langle f,f_1 \rangle f_1 + \langle f,f_2 \rangle f_2$ is bounded linear operator, and calculate his norm.

...Idea: $|Af| \leq ||f|| ||f_1|| ||f_1|| + ||f|| ||f_2|| ||f_2||$ (??)