# Future Books

## Functional Analysis Volume 2

### The spectral theorem for normal compact operators

#### Dzung Minh Ha

No publication date has been set; we are still awaiting files from Professor Ha.

### Tentative list of topics

Measure and integration

Normed and topological vector spaces; Hilbert spaces

Schauder bases

coefficient functionals and basic sequences
equivalent bases

Schauder basis for *C*([a,b], *R*)

The Hahn-Banach theorem and its consequences

Separation theorems

Annihilators and the Banach adjoint

Dual spaces of some well-known spaces

Dual spaces of closed subsapces and quotient spaces

Basic sequences in dual spaces

The bi-dual and reflexivity

Characterizations of reflexivity

Weak and weak star toplogy

Tukey's lemma and Tychonov's theorem on product of compact topological spaces

Weak convergence in *l*^{p}

Weak completeness of reflexive normed spaces

Schur's theorem on the equivalence of weak and strong convergence in
*l*^{1}

A Bolzano-Weierstrass theorem for weak convergence

The Banach-Alaoglu theorem

Operators on Hilbert spaces

Spectral theory of Banach algebras

The spectral radius formula and the spectral mapping theorem

Gelfand-Mazur theorem and Wienner's theorem

Compact operators and finite-rank operators

spectral theory of compact operators

The spectral theorem for compact normal operators on Hilbert space

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