Thursday, **October 18**, 4:30 - 6:00, Jeff 422

Pei-Lun Tseng (Queen's)

Right Hilbert A-modules, part 2

For the last talk, we gave some motivating examples and the definition of
right A-module. We will begin this talk by showing some properties of
A-valued pre inner product, and then we will deduce the process to construct
a right Hilbert A-module. Next, we will introduce the operators on
right Hilbert A-modules, and proving some properties of the corresponding
adjoint operators.

Thursday, **October 11**, 4:30 - 6:00, Jeff 422

Pei-Lun Tseng (Queen's)

Right Hilbert A-modules

Last week, we gave a sketch of proving the GNS construction. We will start
to introduce the matrices over a C*-algebra this week, which is an
application of the GNS construction. Then, we will begin the new topic:
Right Hilbert A-modules. We will deduce the process to construct the inner
product on a right Hilbert A-module H. As long as we have the inner product,
we can consider the orthogonality on H and compare the different between the
scalar case and $A$-valued case..

Thursday, **October 4**, 4:30 - 6:00, Jeff 422

Pei-Lun Tseng (Queen's)

$A$-Valued Theory

In order to study operator-valued probability, we need
some basic knowledge of C*-algebras. In this talk, I am
trying to review what is a C*-algebra. and some
properties of C*-algebras. The GNS construction will be
covered, which is known as the follows: every
C*-algebras can be represented as a algebra of bounded
linear operators on a Hilbert space. This construction
gives us good starting point to study matrices over a
C*-algebra. If time permits, I will introduce right
Hilbert $A$-modules.

Thursday, **September 27**, 4:30 - 6:00, Jeff 422

Jamie Mingo (Queen's)

Operator Values Freeness and Non-commutative functions, II

Free Additive Convolution and Subordination

Last week I reviewed the basic facts of scalar free independence. This week I will continue with a new convolution of probability measures called the free additive convolution. We will use a tool from complex analysis called subordination to get our convolution. It will then lead to a discussion of conditional expectation which will be the basis of operator valued freeness.

Last week I reviewed the basic facts of scalar free independence. This week I will continue with a new convolution of probability measures called the free additive convolution. We will use a tool from complex analysis called subordination to get our convolution. It will then lead to a discussion of conditional expectation which will be the basis of operator valued freeness.

Thursday, **September 20**, 4:30 - 6:00, Jeff 422

Jamie Mingo (Queen's)

Operator Values Freeness and Non-commutative functions

This fall the seminar will be a learning seminar with
lectures by (willing) participants. The theme will be
operator valued freeness. This is the non-commutative
version of conditional independence, now we have
independence over a subalgebra. In many cases the
subalgebras are n x n matrices so this is quite a general
situation.
I will begin by reviewing the basic facts of scalar free
independence. The seminar will follow a recent book by D.
Kaliuzhnyi-Verbovetskyi and V. Vinnikov and some lecture
notes of D. Jekel.

Previous Schedules