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'(

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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 1 (38.98 KiB) Viewed 352 times

Prove the following:

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 2 (18.3 KiB) Viewed 352 times

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.