Descent spectrum equality.

A bounded operator T in a Banach space X is said to satisfy the descent spectrum equality, if the descent spectrum of T as an operator on X coincides with the descent spectrum of T as an element of the algebra B (X) of all bounded linear operators on X. In this paper, we give some conditions under which the equality σ desc (T) = σ desc (T , B (X)) holds for a single operator T. [ABSTRACT FROM AUTHOR]