A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy "Browder's theorem" if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy "a-Browder's theorem" if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which "Weyl's theorem" holds.
|Number of pages||15|
|Journal||Mediterranean Journal of Mathematics|
|Publication status||Published - 2005|
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