Overview
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Explore the second part of a mini-course on Operators on Function Spaces presented by William Ross from the University of Richmond. Delve into advanced topics such as multiplication operators, bilateral shifts, Toeplitz operators, and their matrix representations. Examine the Brown-Halmos theorem, compactness, and analytical Toeplitz operators. Investigate the commutant of the unilateral shift, spectral properties, and kernels of Toeplitz operators. Gain insights into nearly invariant subspaces and conclude with an inspirational result from Hilbert. This 51-minute lecture, part of the Focus Program on Analytic Function Spaces and their Applications, offers a deep dive into complex mathematical concepts for those interested in function space theory and operator algebra.
Syllabus
Intro
Multiplication operators on
All of the multiplication operators?
Matrix representation - Converse
The bilateral shift
Trigger warning
Definition of a Toeplitz operator
Two special Toeplitz operators
Matrix representation of T
Toeplitz matrices
Adjoint
Brown-Halmos theorem
Compactness
Special note
Analytic Toeplitz operators
The commutant of the unilateral shift T.
Back to the spectrum
Kernel of a Toeplitz operator
Nearly invariant
An inspirational result of Hilbert
Taught by
Fields Institute