Banach lattice versions of strict singularity Articles uri icon

authors

  • FLORES, J.
  • LOPEZ-ABAD, J.
  • TRADACETE PEREZ, PEDRO

publication date

  • April 2016

start page

  • 2715

end page

  • 2731

issue

  • 7

volume

  • 270

International Standard Serial Number (ISSN)

  • 0022-1236

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

abstract

  • We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span of any disjoint sequence, coincides with that of lattice strictly singular operators, i.e. those not invertible on any (infinite dimensional) sublattice. New results are given which help to clarify the existing relation between these two classes. (C) 2016 Elsevier Inc. All rights reserved.

subjects

  • Mathematics

keywords

  • disjointly strictly singular operator; lattice strictly singular operator; banach lattice; unconditional sequence; operators; spaces; subspaces