Editing Approximation property (section)

== Examples ==

* Every subspace of an arbitrary product of Hilbert spaces possesses the approximation property.{{sfn | Schaefer|Wolff| 1999 | p=108-115}}  In particular,
** every Hilbert space has the approximation property. 
** every projective limit of Hilbert spaces, as well as any subspace of such a projective limit, possesses the approximation property.{{sfn | Schaefer|Wolff| 1999 | p=108-115}} 
** every [[nuclear space]] possesses the approximation property.
* Every separable Frechet space that contains a Schauder basis possesses the approximation property.{{sfn | Schaefer|Wolff| 1999 | p=108-115}} 
* Every space with a [[Schauder basis]] has the AP (we can use the projections associated to the base as the <math>T</math>'s in the definition), thus many spaces with the AP can be found. For example, the [[lp space|<math>\ell^p</math> spaces]], or the [[Tsirelson space|symmetric Tsirelson space]].