Editing Reflexive space (section)

=== Sufficient conditions ===

;Normed spaces

A normed space that is semireflexive is a reflexive Banach space.{{sfn|Trèves|2006|p=375}}
A closed vector subspace of a reflexive Banach space is reflexive.{{sfn|Narici|Beckenstein|2011|pp=488-491}}

Let <math>X</math> be a Banach space and <math>M</math> a closed vector subspace of <math>X.</math> If two of <math>X, M,</math> and <math>X / M</math> are reflexive then they all are.{{sfn|Narici|Beckenstein|2011|pp=488-491}} This is why reflexivity is referred to as a {{em|three-space property}}.{{sfn|Narici|Beckenstein|2011|pp=488-491}}

;Topological vector spaces

If a [[barreled space|barreled]] locally convex Hausdorff space is semireflexive then it is reflexive.{{sfn|Trèves|2006|pp=372-374}}

The strong dual of a reflexive space is reflexive.{{sfn|Schaefer|Wolff|1999|p=145}}Every [[Montel space]] is reflexive.{{sfn|Trèves|2006|p=376}} And the strong dual of a [[Montel space]] is a Montel space (and thus is reflexive).{{sfn|Trèves|2006|p=376}}