On Browder tuples

Harte, Robin E. and Kitson, Derek (2009) On Browder tuples. Acta Scientiarum Mathematicarum, 75 (3-4). pp. 665-677.

Abstract

In this article we extend the notions of a quasipolar, polar and Browder element in a normed algebra to a multivariable setting. A decomposition result is established for Browder tuples of bounded operators and characterisations in terms of ascent and descent are provided for some special cases. Finally we show that a multivariable spectral mapping theorem holds for a large class of Browder joint spectra.