| 11. | Clearly, all Banach spaces and Fr�chet spaces are F-spaces.
|
| 12. | One can also study the spectral properties of operators on Banach spaces.
|
| 13. | With respect to either of these norms, is a Banach space.
|
| 14. | The construction may also be extended to Banach spaces and Hilbert spaces.
|
| 15. | The general definition for Banach spaces was given by Grothendieck.
|
| 16. | Let X, Y, and Z be Banach spaces.
|
| 17. | A Banach space with a Schauder basis is necessarily bounded approximation property.
|
| 18. | The quotient is a Banach space when is complete.
|
| 19. | Let be a bounded sequence in a Banach space.
|
| 20. | This applies in particular to separable reflexive Banach spaces.
|
