Next:
Locally Convex Spaces and
Functional Analysis Notes
Brian Bockelman
Monday, January 8, 2006:
Locally Convex Spaces and Topological Vector Spaces
Hahn-Banach Separation Theorems
Dual Spaces for LCS
Duality and Weak Topologies
Weak Topologies and Continuous Maps
Polars and the Bipolar Theorem
Subspaces and Quotients for LCS
Topology Review
Basic Definitions
Directed Sets
Separation Properties and Constructing Continuous Functions
Alaoglu's Theorem
Metrizability
Applications of Weak Topologies
Sobcyzk's Theorem
The Stone-Cech Compactification
The Klein-Millman Theorem
Schauder's Fixed Point Theorem
Linear Operators on Banach spaces
Compact Operators on Banach Spaces
Invariant Subspaces:
Spectral Theory
Banach Algebras
Ideals and Invertibility
Spectral Permanance:
Spectrum of a linear operator
Riesz Idempotents
Brian Bockelman 2006-04-21
