Perturbed Browder, Weyl theorems and their variations: Equivalences

Abstract

The presence, or the lack of, SVEP on the holes of the Weyl (resp., a-Weyl) spectrum
of a Banach space operator characterizes Browder and generalized Browder (resp., a-
Browder and generalized a-Browder) theorems for the operator. The isolated points of
the Weyl spectrum (resp., the a-Weyl spectrum, the B-Weyl spectrum and the upper
B-Weyl spectrum) play a similar role in determining Weyl's (resp., a-Weyl's, generalized
Weyl's and generalized a-Weyl's) theorem for the operator. This paper establishes the role
played by the isolated points of these Weyl spectra in establishing equivalences between
Browder, Weyl type theorems, their (recently considered) avatars and perturbations by
commuting Riesz operators.