Probabilistic Operator Algebra Seminar: Commutators close to the identity

Seminar | September 11 | 3:45-5:45 p.m. | 748 Evans Hall

 Jorge Garza Vargas, UC Berkeley

 Department of Mathematics

In the 40's Wielandt and Wintner proved that the commutator of two bounded operators can never equal the identity. Four decades later Popa gave a quantitative version of this result by showing that, if the commutator of two bounded operators is close to the identity, then the norm of these operators is bounded below by half of the logarithm of the reciprocal of the distance between the commutator and the identity. In a recent paper, using only basic tools in operator theory, Terence Tao showed that Popa's bound is almost tight. In this talk we will review this proof.