Introduction to Operator Theory

Department: 
MATH
Course Number: 
7334
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every spring semester

Theory of linear operators on Hilbert space; spectral theory of bounded and unbounded operators; applications

Prerequisites: 
Course Text: 

At the level of Rudin, Functional Analysis

Topic Outline: 
  • Hilbert spaces and operators on Hilbert spaces; elementary properties and examples; projections and idempotents, invariant and reducing spaces
  • Spectral theory; Banach algebras elementary properties; Riesz functional calculus, spectral theory of compact operators, spectral theorem of normal operators
  • Unbounded operators; basic properties and examples, symmetric and self-adjoint operators and the spectral theorem, the Cayley transform
  • Suggested applications
    • Semigroups; Hille-Yoshida's theorem
    • The Fourier transform and differentiation
    • System theory