Affordable Access

Publisher Website

Chapter IV Positive Operators

DOI: 10.1016/s0304-0208(08)70961-7
  • Mathematics


Publisher Summary This chapter presents a theorem that provides sufficient conditions that a non-zero element of Banach algebra should generate a strict locally compact semi-algebra. A theorem is presented in the chapter that states that if the peripheral spectrum of the generator is a set of poles and if the semi-algebra it generates is strict then the spectral radius is a pole of the generator of maximal order in the peripheral spectrum. The sufficient conditions for an element in semi-algebra have its spectral radius in its spectrum. These conditions are phrased in terms of ideals of the semi-algebra. The chapter provides methods that yield the generalizations of the Krein–Rutman theorem. The theorem states that if a bounded irreducible positive linear operator on a Banach space has a peripheral spectrum consisting of poles of finite rank then the spectral radius is an eigenvalue and the associated eigenspace is one dimensional.

There are no comments yet on this publication. Be the first to share your thoughts.


Seen <100 times