A Course in Functional Analysis

[835/1%]

J. B. Conway

Chapter IHilbert Spaces[54/0%]

Section I.1Elementary Properties and Examples[11/0%]

Section I.2Orthogonality[6/0%]

Section I.3The Riesz Representation Theorem[6/0%]

Section I.4Orthonormal Sets of Vectors and Bases[20/0%]

Section I.5Isomorphic Hilbert Spaces and the Fourier Transform for the Circle[9/0%]

Section I.6The Direct Sum of Hilbert Spaces[2/0%]

Chapter IIOperators on Hilbert Space[97/0%]

Section II.1Elementary Properties and Examples[13/0%]

Section II.2The Adjoint of an Operator[16/0%]

Section II.3Projections and Idempotents; Invariant and Reducing Subspaces[12/0%]

Section II.4Compact Operators[14/0%]

Section II.5The Diagonalization of Compact Self-Adjoint Operators[5/0%]

Section II.6An Application: Sturm-Liouville Systems[6/0%]

Section II.7The Spectral Theorem and Functional Calculus for Compact Normal Operators[17/0%]

Section II.8Unitary Equivalence for Compact Normal Operators[14/0%]

Chapter IIIBanach Spaces[102/0%]

Section III.1Elementary Properties and Examples[16/0%]

Section III.2Linear Operators on Normed Spaces[8/0%]

Section III.3Finite Dimensional Normed Spaces[2/0%]

Section III.4Quotients and Products of Normed Spaces[16/0%]

Section III.5Linear Functionals[7/0%]

Section III.6The Hahn-Banach Theorem[10/0%]

Section III.7An Application: Banach Limits[3/0%]

Section III.8An Application: Runge's Theorem[2/0%]

Section III.9An Application: Ordered Vector Spaces[9/0%]

Section III.10The Dual of a Quotient Space and a Subspace

Section III.11Reflexive Spaces[4/0%]

Section III.12The Open Mapping and Closed Graph Theorems[8/0%]

Section III.13Complemented Subspaces of a Banach Space[7/0%]

Section III.14The Principle of Uniform Boundedness[10/0%]

Chapter IVLocally Convex Spaces[71/0%]

Section IV.1Elementary Properties and Examples[24/0%]

Section IV.2Metrizable and Normable Locally Convex Spaces[8/0%]

Section IV.3Some Geometric Consequences of the Hahn-Banach Theorem[15/0%]

Section IV.4Some Examples of the Dual Space of a Locally Convex Space[7/0%]

Section IV.5Inductive Limits and the Space of Distributions[17/0%]

Chapter VWeak Topologies[78/0%]

Section V.1Duality[10/0%]

Section V.2The Dual of a Subspace and a Quotient Space[2/0%]

Section V.3Alaoglu's Theorem[3/0%]

Section V.4Reflexivity Revisited[7/0%]

Section V.5Separability and Metrizability[6/0%]

Section V.6An Application: The Stone-\v{C}ech Compactification[8/0%]

Section V.7The Krein-Milman Theorem[10/0%]

Section V.8An Application: The Stone-Weierstrass Theorem[8/0%]

Section V.9The Schauder Fixed Point Theorem[1/0%]

Section V.10The Ryll-Nardzewski Fixed Point Theorem[2/0%]

Section V.11An Application: Haar Measure on a Compact Group[10/0%]

Section V.12The Krein-Smulian Theorem[6/0%]

Section V.13Weak Compactness[5/0%]

Chapter VILinear Operators on a Banach Space[48/0%]

Section VI.1The Adjoint of a Linear Operator[12/0%]

Section VI.3Compact Operators[21/0%]

Section VI.4Invariant Subspaces[9/0%]

Section VI.5Weakly Compact Operators[6/0%]

Chapter VIIBanach Algebras and Spectral Theory for Operators on a Banach Space[101/0%]

Section VII.1Elementary Properties and Examples[9/0%]

Section VII.2Ideals and Quotients[16/0%]

Section VII.3The Spectrum[7/0%]

Section VII.4The Riesz Functional Calculus[11/0%]

Section VII.5Dependence of the Spectrum on the Algebra[6/0%]

Section VII.6The Spectrum of a Linear Operator[17/0%]

Section VII.7The Spectral Theory of a Compact Operator[6/0%]

Section VII.8Abelian Banach Algebras[18/0%]

Section VII.9The Group Algebra of a Locally Compact Abelian Group[11/0%]

Chapter VIIIC*-Algebras[54/0%]

Section VIII.1Elementary Properties and Examples[4/0%]

Section VIII.2Abelian C*-Algebras and the Functional Calculus in C*-Algebras[7/0%]

Section VIII.3The Positive Elements in a C*-Algebra[25/0%]

Section VIII.4Ideals and Quotients of C*-Algebras[7/0%]

Section VIII.5Representations of C*-Algebras and the Gelfand-Naimark-Segal Construction[11/0%]

Chapter IXNormal Operators on Hilbert Space[127/0%]

Section IX.1Spectral Measures and Representations of Abelian C*-Algebras[16/0%]

Section IX.2The Spectral Theorem[23/0%]

Section IX.3Star-Cyclic Normal Operators[8/0%]

Section IX.4Some Applications of the Spectral Theorem[10/0%]

Section IX.5Topologies on

\mathcal{B}(\mathcal{H})

[6/0%]

Section IX.6Commuting Operators[12/0%]

Section IX.7Abelian von Neumann Algebras[16/0%]

Section IX.8The Functional Calculus for Normal Operators: The Conclusion of the Saga[15/0%]

Section IX.9Invariant Subspaces for Normal Operators[7/0%]

Section IX.10Multiplicity Theory for Normal Operators: A Complete Set of Unitary Invariants[14/0%]

Chapter XUnbounded Operators[62/10%]

Section X.1Basic Properties and Examples[13/8%]

Section X.2Symmetric and Self-Adjoint Operators[10/20%]

Section X.3The Cayley Transform[8/0%]

Section X.4Unbounded Normal Operators and the Spectral Theorem[12/0%]

Section X.5Stone's Theorem[6/0%]

Section X.6The Fourier Transform and Differentiation[9/22%]

Section X.7Moments[4/25%]

Chapter XIFredholm Theory[41/0%]

Section XI.1The Spectrum Revisited[4/0%]

Section XI.2Fredholm Operators[6/0%]

Section XI.3The Fredholm Index[8/0%]

Section XI.4The Essential Spectrum[9/0%]

Section XI.5The Components of

\mathcal{SF}

[5/0%]

Section XI.6A Finer Analysis of the Spectrum[9/0%]