Topics in Operator Theory
- Banach algebras, Spectrum of an element, Representation theorems for commutative and noncommutative Banach algebras
- Spectral mapping theorem for Hermitian and normal operators
- Numerical range of linear operators on Hilbert spaces
- Normal operators, Topologies on B(H), Spectral measures, Commutant, von Neumann algebras, Functional calculus for normal operators
- Compact operators, Hilbert-Schmidt and trace class operators, Dual space of Hilbert-Schmidt and trace class operators
- Non-normal operators, Volterra operator, Bergmann operator, Subnormal operators, Essentially normal operators
- Introduction to von Neumann algebras, Properties and examples, Kaplansky density theorem
- Equivalence of projections Classification of projections Properties of projections
- The structure of Type I von Neumann algebras, The classification of Type I von Neumann algebras
- Operator-valued measurable functions, Some structure theory for continuous algebras
- Reflexive operators on finite dimensional spaces
- Hyperreflexive subspaces and properties
- Reflexivity and duality
- Hypereflexive von Neumann algebras
- Examples and theorems and applications