Date & Time: Friday Sep 14, 4pm (Tea/Coffee at 3:45pm)
Location: Simons Centre, Ground Floor.
Speaker: Arundhathi Krishnan, ISI Bangalore
Title: The spectral theorem
Abstract:
The spectral theorem is a key result in linear algebra and functional analysis, and has a rich history entwined with the evolution of twentieth-century mathematics. It is a result that shows that a certain class of matrices and linear operators can be "diagonalized". These operators- known as normal operators- hence have a simple and elegant form. We look briefly at the development of spectral theory, and at a proof of the finite-dimensional spectral theorem. If time permits, we look at a "simple" perspective on the infinite dimensional spectral theorem as given by Halmos.
References:
1. Halmos, P. R. (1963). What does the spectral theorem say?. *The American Mathematical Monthly*, *70*(3), 241-247.
2. Steen, L. A. (1973). Highlights in the history of spectral theory. *The American Mathematical Monthly*, *80*(4), 359-381.