Event Detail

Event Type: 
Analysis Seminar
Date/Time: 
Monday, May 15, 2017 - 12:00 to 13:00
Location: 
STAG 110

Speaker Info

Institution: 
Undergraduate Student
Abstract: 

This is an expository talk centered on Brown-Douglas-Fillmore theory. We call an operator A on a separable Hilbert space essentially normal if AA*-A*A is a compact operator. It is easy to check that the sum of a normal and a compact is essentially normal. The opposite is not true — for example, unilateral right shift on l^2(N) is essentially normal, although not a sum of a normal and compact. I will state the criteria of an essentially normal operator being a sum of normal and compact, and show how extensions by compact operators come into play in a more general theory.