Real Normal operators and Williamson's Normal Form

Seminarium: 
Dyskretna analiza harmoniczna i niekomutatywna probabilistyka
Osoba referująca: 
Tiju Cherian John (Bangalore)
Data spotkania seminaryjnego: 
czwartek, 12. Lipiec 2018 - 11:30
Sala: 
604
Opis: 
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for real skew-symmetric operators is also proved using elementary methods. The later theorem helps to prove a generalization of Williamson's normal form for bounded positive operators on infinite dimensional separable Hilbert spaces. This has applications in the study of infinite mode Gaussian states.