Methods of ascent and descent in multivariable spectral theory
Citation:
Derek Kitson, 'Methods of ascent and descent in multivariable spectral theory', [thesis], Trinity College (Dublin, Ireland). School of Mathematics, 2009, pp 151Download Item:
Abstract:
In this dissertation the theory of ascent and descent for a linear operator
acting on a vector space is extended to arbitrary sets of operators
and applied to the study of joint spectra for finite commuting systems of
bounded operators acting on a complex Banach space. To each member
of a large class of joint spectra containing the Taylor spectrum, Harte
spectrum, two-sided Slodkowski spectra and split versions we associate
a Browder joint spectrum. We show that these Browder joint spectra
are non-empty, compact-valued, have the projection property and consequently
satisfy a spectral mapping theorem. In the case of the Taylor
spectrum, the associated Browder joint spectrum agrees with that of R.E.
Curto and A.T. Dash ([21]).
Author: Kitson, Derek
Advisor:
Timoney, RichardQualification name:
Doctor of Philosophy (Ph.D.)Publisher:
Trinity College (Dublin, Ireland). School of MathematicsNote:
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Mathematics, Ph.D., Ph.D. Trinity College Dublin.Metadata
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