On the peripheral spectrum of order continuous, positive operators

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Abstract

Let E be an order complete Banach function lattice and T a positive, eventually compact, order continuous operator on E. We study necessary conditions under which the peripheral spectrum of T is fully cyclic in terms of certain bands of the underlying Banach function lattice E. A set of sufficient conditions is also given. Examples are presented to demonstrate our methods.

Original languageEnglish
Pages (from-to)119-130
Number of pages12
JournalPositivity
Volume4
Issue number2
DOIs
StatePublished - Jun 2000

Keywords

  • Order continuous
  • Perron-Frobenius theory
  • Principal T-band

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