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A new derivation of the equation      L ( E , X ∗  ∗  ) = L ( E , X ) ∗  ∗  L(E,{X^{ \ast \ast }}) = L{(E,X)^{ \ast \ast }}       is given, for      dim ⁡  ( E ) &gt; ∞  \dim (E) &gt; \infty       and      X X       a Banach space. From this equation the principle of local reflexivity is derived.

The equation 𝐿(𝐸,𝑋**)=𝐿(𝐸,𝑋)** and the principle of local reflexivity

The equation 𝐿(𝐸,𝑋)=𝐿(𝐸,𝑋) and the principle of local reflexivity