No abstract

The paper contains a complete description of spectrum of disjointness preserving operators on C(K ). As an application we fully describe spectrum of weighted automorphisms of unital uniform algebras.

We describe essential (in particular Fredholm and semi-Fredholm) spectra of operators on Banach lattices of the form T = wU , where w is a central operator and U is a disjointness preserving operator such that its spectrum σ(U ) is a subset of the unit circle. Definition 1.2. Let T be a bounded linear operator on a Banach space X. The semi-Fredholm spectrum of T is σ sf (T ) = {λ ∈ σ(T ) : the operator λI − T is not semi − Fredholm}. The Fredholm spectrum of T is σ f (T ) = {λ ∈ σ(T ) : the operator λI − T is not Fredholm}.

We extend the well known criteria of reflexivity of Banach lattices due to Lozanovsky and Lotz to the class of finitely generated Banach C(K)modules. Namely we prove that a finitely generated Banach C(K)-module is reflexive if and only if it does not contain any subspace isomorphic to either l 1 or c 0 .

No abstract