An introduction to local spectral theory

By K. Laursen, M. Neumann. 2000

816 citations recorded by the source corpus.

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Citations in the corpus

Local Spectral Theory of Linear Operators RS and SR (2006, background): “The local spectrum of T at x is σT (x) = C \ ρT (x), [10].”
Weyl's Theorem, a‐Weyl's Theorem, and Local Spectral Theory (2002, methodology): “An operator T ∈ B(X) has Dunford’s property (C) if the local spectral subspace XT (F) is closed for every closed set F ⊆ ; such operators automatically have the single-valued extension property [17].”
On the Property (gw) (2008, background): “We will say that T ∈ L(X) has the single-valued extension property at λ0, (SVEP for short) if for every open neighborhood U of λ0, the only analytic function f : U → X which satisfies the equation: (T − λI)f (λ )=0 , for all λ ∈ U is the function f ≡ 0 .T ∈ L(X) is said to have the SVEP if T has the”
On local spectral properties of complex symmetric operators (2011, background): “The proof of the converse statement follows from [22].”
Classes of operators satisfying a-Weyl's theorem (2005, background): “[26] K. B. Laursen and M. M. Neumann, Introduction to Local Spectral Theory , Clarendon Press, Oxford, 2000.”
On Drazin invertibility (2008, background): “This property has an important role in local spectral theory; see the recent monographs by Laursen and Neumann [20] and Aiena [1].”
DT-operators and decomposability of Voiculescu's circular operator (2002, unknown): “E-mail: haagerup@imada.sdu.dk”
Invariant subspaces for operators in a general II1-factor (2006, background): “9.1 Theorem. [ LN , Proposition 1.2.23] Let T be a bounded operator on a Hilbert space H. Then the following are equivalent:”
Perturbation of spectra of operator matrices and local spectral theory (2006, unknown): “See also [15] for more details.”
REAL PALEY―WIENER THEOREMS AND LOCAL SPECTRAL RADIUS FORMULAS (2008, background): “, [44], from which the material below on the bounded case is mostly taken.”