Abstract
In this paper, we introduce the left (resp. right) Browder elements in a semiprime, complex and unital Banach algebra A. It is established that (i) a∈A is left Browder if and only if a is relatively regular and the left quasinilpotent part of a (or, the left hyperkernel of a) is of finite order; (ii) the spectral mapping theorem holds for the left Browder spectrum; (iii) the set of all left Browder elements is an open multiplicative semigroup; (iv) the left Browder spectrum is stable under commuting Riesz perturbations; (v) Riesz elements are characterized by means of the invariance of the left Browder spectrum under commuting perturbations; (vi) the Kato decomposition for left Browder elements in primitive C* algebras is provided. Similar results hold for the right Browder elements and the right Browder spectrum.
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