The Taylor-Browder spectrum on prime C*-algebras.

We provide a formula for the Taylor–Browder spectrum of a pair (L a , R b ) of left and right multiplication operators acting on a prime C*-algebra with non-zero socle. We also compute ascent and descent for multiplication operators on a prime ring, characterise Browder elements in a prime C*-algebra and discuss upper semicontinuity for the Browder spectrum