Stephen Power (Lancaster): 

<BR><BR>

Manifolds of Hilbert space projections. 

<BR><BR>

ABSTRACT: 

<BR><BR>

Various contexts in operator theory often give rise to a finitely
parametrised set of projections which, with the strong operator
topology, forms a topological manifold. (For an easy example
consider the 1-dimensional invariant subspaces of the backward
shift.) A particularly striking isolated example is the so-called
Fourier-Plancherel sphere which arises as natural "continuation"
of the quarter sphere that corresponds to the right translation
invariant subspaces on the line that are also "Beurling subspaces"
(ie. unimodular times the Hardy space). Rupert Levene and I have
developed a new unified approach to such unimodular function
projection manifolds which covers this (and other extant ad hoc
examples). The core technique is an understanding of so-called
"strange limits" of projections in terms of oscillatory integrals.
As a consequence we obtain many other inequivalent 2-spheres (and
n-spheres) of projections. In the talk I will sketch these issues
as well as intriguing problems of differential structure. (The FP
sphere is as smooth as smooth can be away from the poles.)