COLLOQUIUM
Characterization of compact
and self-adjoint operators,
and study of positive
operators on a Banach space
over a non-Archimedean
field
Prof. Khodr Shamseddin
University of Manitoba
Abstract
Let C be the complex Levi-Civita field and let c0 (C) or, simply, c0
denote the space of all null sequences x = (an ), an ∈ C. In this talk,
we define a natural inner product on c0 which induces the sup-norm of
c0 . Unlike classical Hilbert spaces, c0 is not orthomodular with respect
to this inner product, so we characterize those closed subspaces of c0
with an orthonormal complement; such a subspace defines a special kind
of projection, the so-called normal projection. We present
characterizations of normal projections, adjoint and self- adjoint operators,
and compact operators on c0. Then we study in details the properties of
positive operators on c0 , which we then use to introduce a partial order
on the B ∗ -algebra of compact and self-adjoint operators on c0 and study
the properties of that partial order.
Department of
Mathematics
Friday,
August 31st, 2012
4:00 p.m.
204 Morgan Hall
Refreshments will be
served at 3:45 p.m.