Strictly singular and power-compact operators on Banach lattices Articles uri icon

authors

  • FLORES, JULIO
  • HERNÁNDEZ, FRANCISCO L.
  • SEMENOV, EVGUENI M.
  • TRADACETE PEREZ, PEDRO

publication date

  • March 2012

start page

  • 323

end page

  • 352

issue

  • 1

volume

  • 188

International Standard Serial Number (ISSN)

  • 0021-2172

Electronic International Standard Serial Number (EISSN)

  • 1565-8511

abstract

  • Compactness of the iterates of strictly singular operators on Banach lattices is analyzed. We provide suitable conditions on the behavior of disjoint sequences in a Banach lattice, for strictly singular operators to be Dunford-Pettis, compact or have compact square. Special emphasis is given to the class of rearrangement invariant function spaces (in particular, Orlicz and Lorentz spaces). Moreover, examples of rearrangement invariant function spaces of fixed arbitrary indices with strictly singular non power-compact operators are also presented.