Definition:Reflexive Space

Definition

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.

Sources

• Weisstein, Eric W. "Reflexive Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReflexiveSpace.html
• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $26.1$: The Second Dual