A collection of Browder joint spectra
Derek Kitson (Trinity College, Dublin)
Tuesday 2nd June, 2009 16:00-17:00 214
The classical notions of ascent and descent for a linear operator on a vector space can be extended to arbitrary collections of operators. Using this fact we construct a Browder joint spectrum for commuting n-tuples of bounded operators on a complex Banach space. This Browder joint spectrum is compact-valued and satisfies a multivariable spectral mapping theorem. In fact we arrive at a collection of Browder joint spectra with these properties and provide a new characterisation for the Taylor-Browder spectrum. Finally we will consider applications to operator equations.