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Matrix Editions future books

 

For information on volume 1:

Functional Analysis Volume 1: A Gentle Introduction

In preparation:

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


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