Fredholm and Local Spectral Theory, with Applications to Multipliers

By P. Aiena. 2004

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On Drazin invertibility (2008, background): “This implies, again by Theorem 3.4 of [1], that also p ( T [ n ] ) ∞ , so that T [ n ] is Browder and hence T is B -Browder.”
On local spectral properties of complex symmetric operators (2011, background): “Then T is a complex symmetric operator by [26], but T = S∗ ⊕ S satisfies neither Weyl’s theorem nor Browder’s theorem (see [1]).”
Additive Maps Preserving Local Spectrum (2006, background): “Our references are the books of Aiena [ 1 ] and of Laursen and Neumann [12].”
Complex symmetric weighted composition operators on H2(D) (2014, background): “An operator T ∈ L(H) is said to have the single-valued extension property at z0 if for every neighborhood G of z0 and any H-valued analytic function f on G such that (T − z)f(z) ≡ 0 on G, we have f(z) ≡ 0 on G (see [1,5,24] for more details).”
Classes of operators satisfying a-Weyl's theorem (2005, background): “Recall that every semi-Fredholm operator is of Kato type, by the classical result of Kato [25] (see also Chapter 1 of [1]).”