⇒ Name: Functional Analysis - Lecture Notes
⇒ Author(s): Douglas N. Arnold
⇒ Pages: 36
⇒ Format : PDF
⇒ Size: 292 KB

I. Vector spaces and their topology

Subspaces and quotient spaces

Basic properties of Hilbert spaces

II. Linear Operators and Functionals

The Hahn–Banach Theorem

Duality

III. Fundamental Theorems

The Open Mapping Theorem

The Uniform Boundedness Principle

The Closed Range Theorem

IV. Weak Topologies

The weak topology

The weak* topology

V. Compact Operators and their Spectra

Hilbert–Schmidt operators

Compact operators.

Spectral Theorem for compact self-adjoint operators

The spectrum of a general compact operator

VI. Introduction to General Spectral Theory

The spectrum and resolvent in a Banach algebra

Spectral Theorem for bounded self-adjoint operators

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