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Here are a few more consequences:

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• The norm of T* $T^*$ equals the norm of T

-X $T$

• $X$ reflexive and M $M$ closed in X $X$ implies M $M$ reflexive

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• If X $X$ Banach then X* $X^*$ reflexive iff X $X$ is reflexive

-X*

• $X^*$ separable implies X $X$ separable

-

• If X $X$ Banach and $T \in B(X) B(X)$ then T $T$ invertible iff T* $T^*$ invertible
1

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