*Functional
Analysis Volume 2:*

*The
spectral theorem for normal compact operators*

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 operatorsand finite-rank operators

spectral theory of compact operators

The spectral theorem for compact normal operators on Hilbert space

If you would like to be
notified when this book becomes available, please sign up
here.

Top of page

Back to Home