Arkady Kitover, Department of Mathematics, Community College of Philadelphia, 1700 Spring Garden Street Philadelphia, PA 19154, USA, E-mail address: akitover@ccp.cc.pa.us

Peripheral spectrum of positive operators and generalizations of Jentzsch’s theorem

The main result. Theorem. Let X be a Banach lattice and T : X → X be a positive operator. If the peripheral spectrum of T consists of a finite number of eigenvalues of T then it is cyclic.

Moreover, if X has the Fatou property, T is sequetially order continuous, and for any non-zero positive u ∈ X T u is a weak unit in X then the peripheral spectrum consists of only one point r(T) and the corresponding eigenspace is one-dimensional.