I'm reading a book about Functional Analysis, and now I've reached to the part about dual operators.
I'm having some difficulties understanding the following definition -
Why $A^*$ is $Y^*\rightarrow X^*$? We know that $\phi \in Y^*$, i.e., $\phi:Y\rightarrow Y$ and bounded. So the image of $\phi(Ax)$ should be in $Y^*$, shouldn't it?
How come it's in $X^*$?
($X^*$ is reffered here as the space of all bounded linear functionals on $X$).