Let X,Y be normed spaces and T E L(X,Y). The transpose of T, T', is the linear operator from Y' into X' defined by T'y'(
Posted: Tue Sep 07, 2021 7:24 am
Let X,Y be normed spaces and T E L(X,Y). The transpose of T, T', is the linear operator from Y' into X' defined by T'y'(X) = y'(Tx), Y'E Y', E X, i.e., T'y' = y'T. We have the following properties of the
3. Let X,Y be Banach spaces and T E L(X,Y). Show that if T is one-one and has closed range, then T' is onto.