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
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