I know how to characterize the continuity of a linear operator $T:X \to Y$ between normed spaces when I am working in the context of weak-to-weak, norm-to-norm and weak$^*$-to-weak$^*$ continuity. Nevertheless, I do not know any Functional Analysis book where it is characterized the norm-to-weak, weak-to-norm, weak-to-weak$^*$,... continuity of a linear operator. Could someone recommend me a book (with proofs) about that?
Thanks!