Lecture notes to the course Functional Analysis 2
Summer semester 2021/2022
Lecture notes to the preceeding course
Functional Analysis 1 (2021/2022)
V. Bounded and unbounded operators on a Hilbert space
A proof of Proposition V.1
A proof of Proposition V.2
Proofs of Lemma V.3 and Proposition V.4
A proof of Proposition V.5
A proof of Proposition V.6
A proof of Proposition V.7
A proof of Theorem V.8
Proofs of Theorem V.8, Proposition V.10 and Theorem V.11
| V.2 Unbounded operators between Banach spaces - | Czech, English |
Explanation of the final remark
On variants of the definition of the resolvent set
| V.5 Symmetric operators and Cayley transform - | Czech, English |
A proof of Theorem V.35
Remarks and questions on deficiency indices
| Problems to Chapter V - | here |
VI. Spectral measures and spectral decompositions
| VI.1 Measurable calculus for bounded normal operators - | Czech, English |
Proof of Proposition VI.1
Construction of measurable calculus and spectral measure, to Lemma VI.3
Proof of Theorem VI.4
| VI.2 Integral with respect to a spectral measure - | Czech, English |
A proof of Lemma VI.5
A proof of Lemma VI.6
A proof of Theorem VI.8
Proofs of Lemma VI.9 and COrollary VI.10
A proof of Theorem VI.11
A proof of Theorem VI.12
A proof of Proposition VI.13
| VI.3 Spectral decomposition of a selfadjoint operator - | Czech, English |
Proofs of Lemma VI.15-Corollary VI.18
A proof of Lemma VI.19
A proof of Lemma VI.20
Proofs of Theorem VI.21 and its corollaries
Proofs of Proposition VI.24 and Theorem VI.25
A proof of Theorem VI.26
A proof of Theorem VI.27
| Problems to Chapter VI - | here |
| Example - selfadjoint Laplace operators - | here |
VII. More on locally convex topologies
| VII.1 Lattice of locally convex topologies
and topologies agreeing with duality | - Czech, English |
Proofs of Lemma VII.2 and Propositition VII.3
Proofs of Lemmata VII.4 and VII.5
Proofs of Theorem VII.6 and Propositition VII.7
| VII.2 bw*-topology and Krein-mulyan theorem - | Czech, English |
A proof Proposition VII.11
Proofs of Theorem VII.12 and its corollaries
A proof Theorem VII.15
Proofs of Lemma VII.17 and Theorem VII.18
A proof of Proposition VII.19
A proof of Proposition VII.21
Proofs of Proposition VII.22 and Theorem VII.23
Three examples concerning extreme points
| VII.4 Weakly compact sets and operators
in Banach spaces | - Czech, English |
An example of a sequence without convergent subsequence but with a convergent subnet
Distinguishing notions similar to compactness
A proof of Lemma VII.25
A proof of Theorem VII.26 (including VII.27-VII.29)
A proof of Theorem XI.33
A proof of Theorem XI.34
| Problems to Chapter VII - | here |
