Foreword

1.Linear Spaces

2.Linear Maps

3.The Hahn-Banach Theorem

4.Applications of the Hahn-Banach theorem

5.Normed Linear Spaces

6.Hilbert Space

7.Applications of Hilbert Space Results

8.Duals of Normed Linear Speaces

9.Applications of Duality

10.Weak Convergence

11.Applications of Weak Convergence

12.The Weak and Weak Topologies

13.Locally Convex Topologies and the Krein-Milman Theorem

14.Examples of Convex Sets and Their Extreme Points

15.Bounded Linear Maps

16.Examples of Bounded Linear Maps

17.Banach Algebras and their Elementary Spectral Theory

18.Gelfand's Theory of Commutative Banach Algebras

19.Applications of Gelfand's Theory of Commutative Banach Algebras

20.Examples of Operators and Their Spectra

21.Compact Maps

22.Examples of Compact Operators

23.Positive compact operators

24.Fredholm's Theory of Integral Equations

25.Invariant Subspaces

26.Harmonic Analysis on a Halfline

27.Index Theory

28.Compact Symmetric Operators in Hilbert Space

29.Examples of Compact Sysmmetric Operators

30.Trace Class and Trace Formula

31.Spectral Theory of Symmetric,Normal,and Unitary Operators

32.Spectral Theory of Self-Adjoint Operators

33.Examples of Self-Adjoint Operators

34.Semigroups of Operators

35.Groups of Unitary Operators

36.Examples of Strongly Continuous Semigroups

37.Scattering Theory

38.A Theorem of Beurling

A.Riesz-Kakutani representation theorem

B.Theory of distrbutions

C.Zorn's Lemma

Author Index

Subject Index