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Event Type:

Analysis Seminar

Date/Time:

Monday, May 15, 2017 - 12:00 to 13:00

Location:

STAG 110

Guest Speaker:

Andrey Blinov

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.