ESSENTIAL SPECTRA THROUGH LOCAL SPECTRAL THEORY

Based on a nice observation of Eschmeier, this is a study of the use o f local spectral theory in investigations of the semi-fredholm spectru m of a continuous linear operator, We also examine the retention of th e semi-Fredholm spectrum under weak intertwining relations; it is show n, inter alias, that if two decomposable operators are intertwined asy mptotically by a quasi-affinity then they have identical semi-Fredholm spectra. The results are applied to multipliers on commutative semisi mple Banach algebras.