A locally convex topological vector space is reflexive when its canonical evaluation map to its continuous bidual is an isomorphism with the specified strong dual topologies. For a Banach space, this reduces to surjectivity of the canonical map and gives a reflexive Banach space.
In the context of functional analysis and topology, a reflexive space typically refers to a type of Banach space that is isomorphic to its dual. To elaborate, a Banach space \( X \) is said to be reflexive if the natural embedding of \( X \) into its double dual \( X^{**} \) (the dual of the dual space \( X^* \)) is surjective.
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