… We establish for a bounded linear operator defined on a Banach space … ’s theorem and
with another variant of it, a-Weyl’s theorem. We show that Weyl’s theorem, a-Weyl’s theorem and …

… theorem holds for the set σa(T)\πa0(T) and for all analytic functions which are not constant
on the … from [5] and [7], we say that an operator T on X obeys a-Weyl’s theorem provided that …

… We say that a-Weyl’s theorem holds for T g BH if there is equality … M-hyponormal then a-Weyl’s
theorem holds for f T for every f g Ž … Ž Ž .. 3 a-Weyl’s theorem holds for f T for eery f g H T . …

… In general, we cannot expect that a-Weyl’s theorem necessarily holds for operators having
the single-valued extension property. Consider the quasinilpotent operator T on l2 given by (…

… f is not constant on the connected components of its domain, we prove that a-Weyl’s theorem
holds for f(T). … In Section 3 we prove a perturbation theorem for a-Weyl’s theorem. Namely, if …

… weyl quoteright s theorem .. 29 2 period .. Weyl quoteright s theorems We first b egin by
establishing several equivalences for every bounded op hyphen erators defined on Banach …

… We introduce the class of operators on Banach spaces having prop… a- Weyl’s theorem holds
for every decomposable operator having property (H). We also show that a-Weyl’s theorem …

… on a Banach space X satisfies generalized a-Weyl’s theorem … T + F satisfies generalized
a-Weyl’s theorem if and only if Ea(… on a Banach space satisfies generalized a-Weyl’s theorem …

… ’s theorem and a-Weyl’s theorem on Banach spaces … theorem and a-Weyl’s theorem for T
∗ are equivalent, and analogously, if T∗ has SVEP then Weyl’s theorem and a-Weyl’s theorem …

… is a 2 × 2 upper triangular matrix on the Hilbert space H ⊕ K, then a-Weyl’s theorem for A …
how a-Weyl’s theorem and a-Browder’s theorem survive for 2 × 2 operator matrices on the …