Journal of Operator Theory
Volume 77, Issue 2, Spring 2017 pp. 481-501.
Essential spectrum and Fredholm properties for
operators on locally compact groups
Authors:
Marius Laurentiu Mantoiu
Author institution: Departamento de Matematicas, Facultad de Ciencias,
Universitad de Chile, Santiago, 7800003, Chile
Summary: We study the essential spectrum and Fredholm
properties of certain integral
and pseudo-differential operators associated to non-commutative locally
compact groups $\G$. The techniques involve crossed product
$C^*$-alge\-bras. We extend previous results on the structure of the
essential
spectrum to self-adjoint operators belonging (or affiliated) to the
Schr\"odinger representation of certain crossed products. When the group
$\G$
is unimodular and type I, we cover a new class of global pseudo-differential
differential operators with operator-valued symbols involving the unitary
dual
of $\G$.
We use recent results of Nistor, Prudhon and Roch on the role of families of
representations in spectral theory and the notion of quasi-regular dynamical
system.
DOI: http://dx.doi.org/10.7900/jot.2016may02.2110
Keywords: locally compact group, pseudo-differential operator,
$C^*$-algebra, dynamical system, essential spectrum, Fredholm operator
Contents
Full-Text PDF