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 subspaces 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 l¹
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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