| ÖÇ1 | Learn and apply the Hahn-Banach theorem from the fundamental theorems of functional analysis. |
| ÖÇ2 | Learn and apply the Open Mapping theorem from the fundamental theorems of functional analysis. |
| ÖÇ3 | Learn and apply the Closed Graph theorem from the fundamental theorems of functional analysis. |
| ÖÇ4 | Learn and apply the Uniform Boundedness Principle, one of the fundamental theorems of functional analysis. |
| ÖÇ5 | Learn and apply the inner product function and its properties for Hilbert spaces. |
| ÖÇ6 | Learn and apply series related to orthonormal sequences and sets in Hilbert spaces. |
| ÖÇ7 | Be able to represent functionals in Hilbert spaces. |
| ÖÇ8 | Can determine the Hilbert dual of an operator in Hilbert spaces. |
| ÖÇ9 | Learns and applies S-linear transformations. |
| ÖÇ10 | Learns the spectrum and spectral radius of Banach Algebras. |