Faculty of Mathematics and Physics

Functional Analysis 2

Information in Student Information System


Organization of the course


Content of the course, expected knowledge and connections to other courses


Recommended literature


Lecture notes


Credit requirements
(including statistical data)


Content of the lectures and classes


Conditions from exams
(including statistical data)

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 -

X.2 Spectrum of an unbounded operator -

X.3 Operators on a Hilbert space -

X.4 Symmetric operators and Cayley transform -

X.5 Integral with respect to a spectral measure -

        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 -

        Proofs of Proposition X.32 and Theorem X.33

        Proofs of Lemma X.34 - Corollary X.37

X.7 Unbounded normal operators

        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 -

        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) -

Example - selfadjoint Laplace operators -


XI. More on locally convex topologies

XI.1 Lattice of locally convex topologies
       and topologies agreeing with duality

        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-Šmulyan theorem -

        A proof Proposition XI.11

        Proofs of Theorem XI.12 and its corollaries

        A proof Theorem XI.15

XI.3 Compact convex sets -

        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

        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) -