**"****The Commutant of the Multi-Shift on Besov Hilbert (Weighted
Symmetric Fock) Spaces****"**

By

** Abstract:** The commutant
of a set of operators on Hilbert space is the unital
algebra of operators on the same Hilbert space that commute with each operator
in the set. Sarason in 1967 showed that the commutant of the shift on the Hardy space H^2 of the disc
is bounded holomorphic functions viewed as multipliers
on H^2. By the work of Shields on weighted shifts in 1974, the commutant of the shift on every Besov
Hilbert space F_q on the disc is the multiplier
algebra of F-q. We extend this result to the case of the multi-shift on
the Besov-Hilbert spaces on the unit ball of C^n.

**Date: ****Wednesday, April 24, 2013**

**Time: ****14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.