Event time:
Tuesday, September 20, 2016 - 12:15pm to 1:15pm
Location:
AKW 200
Speaker:
Stefan Steinerberger
Speaker affiliation:
Yale University
Event description:
We discuss a series of classical inequalities in matrix/operator theory; a suitable representative is due to Alan McIntosh and reads
||AXB||^2 = ||A^2X|| ||XB^2||,
where A,B are s.p.d. matrices and X is arbitrary. Inequalities of these types tend to have short and simple proofs (which is good) that do not provide much insight (which is bad). We give a slightly more complicated proof using complex analysis and Fourier series that gives a lot more insight – in particular, we characterize cases of equality (which were unknown) and provide improved inequalities that incorporate information about the spectra of the operators.
Special note:
ANALYSIS SEMINAR