Lecture notes to the course Functional Analysis 2
Summer semester 2016/2017
Lecture notes to the preceeding courses
Introduction to Functional Analysis (2015/2016) (only in Czech)
Functional Analysis 1 (2016/2017)
X. Unbounded operators on a Hilbert space
X.1 Unbounded operator between Banach spaces - | item($czo,$eno) ?>
|
X.2 Spectrum of an unbounded operator - | item($czo,$eno) ?>
|
X.3 Operators on a Hilbert space - | item($czo,$eno) ?>
|
X.4 Symmetric operators and Cayley transform - | item($czo,$eno) ?>
|
X.5 Integral with respect to a spectral measure - | item($czo,$eno) ?>
|
A proof of Lemma X.25
A proof of Theorem X.27
A proof of Theorem X.28
A proof of Theorem X.29
A proof of Theorem X.30
X.6 Spectral decomposition of a selfadjoint operator - | item($czo,$eno) ?>
|
Proofs of Proposition X.32 and Theorem X.33
Proofs of Lemma X.34 - Corollary X.37
X.7 Unbounded normal operators | item(" - ".$czo," - ".$eno) ?>
|
A proof of Lemma X.38
A proof of Lemma X.39
A proof of Theorem X.40 and its corollaries
X.8 Complements to unbounded operators - | item($czo,$eno) ?>
|
Proofs of Proposition X.43 and Theorem X.44
A proof of Theorem X.45
A proof of Theorem X.46
Problems to Chapter X (to be possibly completed) - | item($czo,$eno) ?>
|
Example - selfadjoint Laplace operators - | item($czo,$eno) ?>
|
XI. More on locally convex topologies
XI.1 Lattice of locally convex topologies and topologies agreeing with duality | item("- ".$czo,"- ".$eno) ?>
|
Proofs of Lemma XI.2 and Propositition XI.3
Proofs of Lemmata XI.4 and XI.5
Proofs of Theorem XI.6 and Propositition XI.7
XI.2 bw*-topology and Krein-mulyan theorem - | item($czo,$eno) ?>
|
A proof Proposition XI.11
Proofs of Theorem XI.12 and its corollaries
A proof Theorem XI.15
XI.3 Compact convex sets - | item($czo,$eno) ?>
|
Proofs of Lemma XI.17 and Theorem XI.18
A proof of Proposition XI.19
Proofs of Proposition XI.21
A proof of Proposition XI.22 and Theorem XI.23
XI.4 Weakly compact sets and operators in Banach spaces | item("- ".$czo,"- ".$eno) ?>
|
A proof of Lemma XI.25
A proof of Theorem XI.26 (including XI.27-XI.29)
A proof of Theorem XI.33
A proof of Theorem XI.34
Problems to Chapter XI (may be completed) - | item($czo,$eno) ?>
|