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Title of Journal: Positivity

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Abbravation: Positivity

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Springer Basel

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DOI

10.1016/0921-4526(91)90024-9

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1572-9281

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Domination by ergodic elements in ordered Banach a

Authors: S Mouton K Muzundu
Publish Date: 2013/04/17
Volume: 18, Issue: 1, Pages: 119-130
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Abstract

We recall the definition and properties of an algebra cone in an ordered Banach algebra OBA and continue to develop spectral theory for the positive elements An element a of a Banach algebra is called ergodic if the sequence of sums sum k=0n1 fracakn converges If a and b are positive elements in an OBA such that 0le ale b and if b is ergodic an interesting problem is that of finding conditions under which a is also ergodic We will show that in a semisimple OBA that has certain natural properties the condition we need is that the spectral radius of b is a Riesz point relative to some inessential ideal We will also show that the results obtained for OBAs can be extended to the more general setting of commutatively ordered Banach algebras COBAs when adjustments corresponding to the COBA structure are made

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Other Papers In This Journal:
  1. Order-unit-metric spaces
  2. The Radon–Nikodym Property for Tensor Products of Banach Lattices
  3. Odd Degree Polynomials on Real Banach Spaces
  4. Positive bases in spaces of polynomials
  5. Regular orbits and positive directions
  6. Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem
  7. A new application of non-increasing sequences
  8. On the lower semicontinuity of the solution mappings to a parametric generalized strong vector equilibrium problem
  9. A class of $$\ell ^p$$ saturated Banach spaces
  10. On the Structure of the Completion of a Normed Lattice
  11. Pentadiagonal Oscillatory Matrices with Two Spectrum in Common
  12. The essential spectral radius of Volterra operators and an application to Volterra-Hammerstein functional inclusions
  13. An iterative algorithm for finding a common solution of fixed points and a general system of variational inequalities for two inverse strongly accretive operators
  14. Perturbation of Transition Functions and a Feynman-Kac Formula for the Incorporation of Mortality
  15. Statistical approximation by double sequences of positive linear operators on modular spaces
  16. Modules and extremal completely positive maps
  17. Positive solutions of semi-positone nonlinear operator equations in Banach spaces with lattice structure
  18. A characterization of positively decomposable non-linear maps between Banach lattices
  19. Positive solutions for fractional differential systems with nonlocal Riemann–Liouville fractional integral boundary conditions
  20. Coupled coincidence point results on generalized distance in ordered cone metric spaces
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