Im(F)⊂Im(G)
Equivalent to
∃γ: ,|| F∗z∗∥ <γ || G∗z∗∥
∀z∗∈Z∗
I want proof this lemma
Let V, W and Z be three Banach reflexive spaces. And F∈L(V,Z), G∈L(W,Z). Then the following are equivalent.
Im(F)⊂Im(G)
.
∃γ : || F∗z∗∥ < γ ||G∗z∗∥
∀z∗∈Z∗
.
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