Everyone welcome.  Refreshments will be served in the Math
Lounge before the exam.


Monday, April 4, 2011, 4:10 - 5:00 p.m.,
in BA 6183, 40 St. George Street

PhD Candidate:  Barry Rowe

PhD Advisor:  Peter Rosenthal

Thesis Title:  The Left Regular Representation of a Semigroup

Thesis Abstract:

As with groups, one can study the left regular representation L(S) of a 
semigroup S. Specifically, I will consider the Hilbert space given by 
l_2(S), and the weak operator topology closure of the algebra generated 
by the operators L_s, where L_s acts as left translation by s on the 
basis S.  If one considers such representations, then it is natural to 
ask similar questions to the well known case where S is a group.

I start by formulating several questions in the semigroup case and then 
work toward understanding the structure of the representations given.  
Most of this concerns the problem of describing what the images of the 
elements in the semigroup can look like in this representation 
(specifically, what operators can arise as an L_s from some s in a 
semigroup S).  Some additional results concerning the problem of 
determining when the algebra L(S) is reflexive (that is, when L(S) 
contains all the operators whose lattice of invariant subspaces 
contains the lattice of invariant subspaces of L(S)), and results 
concerning a universal algebra of such representations are also given.


no comment as of now

Sorry, comments closed.