Davies E.B. Spectral Theory

Department of Mathematics King’s College (London), 2004. - 137 pages.Summary of Results from Operator Theory
Banach Spaces
Bounded Linear Operators
A Functional Calculus
Topologies on Banach Spaces
Lp Spaces
Compact linear Operators
Hilbert-Schmidt and Trace Class Operators
Bases of Banach Spaces
Unconditional Bases
Approximation by Smooth Functions
The Fourier TransformSemigroups and Generators
Basic Properties of Semigroups
Other Continuity Conditions
Norm Continuity
Trace Class Semigroups
Semigroups on Dual Spaces
Differentiable and Analytic Vectors
Some Standard ExamplesResolvent Operators
Elementary Properties of Resolvents
Spectral Theory
Pseudospectra of Operator Pencils
Numerical Range
Long Time Growth Bounds
Classification of Generators
Short Time Growth Bounds
Subordinated Semigroups
Bounded Holomorphic Semigroups