Here are a few more consequences:

-The norm of T* equals the norm of T

-X reflexive and M closed in X implies M reflexive

-If X Banach then X* reflexive iff X is reflexive

-X* separable implies X separable

-If X Banach and T in B(X) then T invertible iff T* invertible

Here are a few more consequences:

• The norm of $T^*$ equals the norm of $T$
• $X$ reflexive and $M$ closed in $X$ implies $M$ reflexive
• If $X$ Banach then $X^*$ reflexive iff $X$ is reflexive
• $X^*$ separable implies $X$ separable
• If $X$ Banach and $T \in B(X)$ then $T$ invertible iff $T^*$ invertible