Definition:Reflexive Space

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Let $\struct {X, \norm \cdot_X}$ be a normed vector space.

Let $\struct {X^{\ast \ast}, \norm \cdot_{X^{\ast \ast} } }$ be the second normed dual of $\struct {X, \norm \cdot_X}$.

Let $J : X \to X^{\ast \ast}$ be the evaluation linear transformation.

We say that $X$ is reflexive if and only if:

$J$ is an isometric isomorphism.

Also see

  • Results about reflexive spaces can be found here.