Mathematics Colloquium
Speaker: Sundaram Thangavelu, Indian Institute of Science, Bangalore
Host: Sanjoy Pusti
Title: On points of contention between two families of operators
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, October 08
Venue: Ramanujan Hall
Abstract: Let $ \mathcal{H} $ be a Hilbert space and $ \mathcal{F}_j, j =1,2 $ two families of bounded linear operators acting on $ \mathcal{H}.$ We say that a vector $ u \in \mathcal{H} $ is a point of contention between $ \mathcal{F}_1$ and $ \mathcal{F}_2 $ if for any $ T \in \mathcal{F}_1 $ and $ S \in \mathcal{F}_2, $ the condition $ Tu = Su $ forces both $ T $ and $ S $ to be contstant multiple of the identity operator. We explain this phenomenon when $ \mathcal{H} $ is either the Labesgue space $ L^2(\R^n) $ or the Fock space $ \mathcal{F}(\C^n).$