Mini-course on Operators on Function Spaces - Part 1

Explore a comprehensive mini-course on operators in function spaces, focusing on the Volterra operator. Delve into its properties, including boundedness, compactness, spectrum, and numerical range. Examine the operator's commutant, invariant subspaces, and complex symmetry. Investigate the matrix representation, Hardy's inequality, and the Cesaro matrix. Learn about the adjoint formula, eigenvalues, and spectrum of the Cesaro operator. Discover its subnormal nature and potential generalizations. Gain valuable insights from William Ross of the University of Richmond in this 54-minute lecture, part of the Fields Institute's Focus Program on Analytic Function Spaces and their Applications.

Intro
The Volterra operator
V is bounded
The role of VV
Compactness
The spectrum of V
The numerical range of V
The commutant
Invariant subspaces - the Gelfand problem
V is complex symmetric
Matrix representation of V
Hardy's inequality
The Cesaro matrix
Adjoint formula
Eigenvalues
Spectrum (and numerical range)
The Cesaro operator is subnormal
Generalizations