ACTA issues

On Browder tuples

R. E. Harte, D. Kitson

Acta Sci. Math. (Szeged) 75:3-4(2009), 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.

AMS Subject Classification (1991): 47A13, 47A60, 47A10

Keyword(s): Browder spectrum, joint spectrum, spectral mapping theorem

Received September 23, 2008, and in revised form March 27, 2009. (Registered under 6434/2009.)