On the sum of narrow and finite-rank orthogonally additive operators

  • H. I. Humenchuk

Abstract

It is well known that the sum of two linear continuous narrow operators in the spaces Lp with 1 < p < ∞ need not be narrow. However, the sum of narrow and compact linear continuous operators is narrow. In a recent paper, M. Pliev and M. Popov started the investigation of nonlinear narrow operators and, in particular, of orthogonally additive operators. As our main result, we prove that the sum of a narrow orthogonally additive operator and a finite-rank laterally-to-norm continuous orthogonally additive operator acting from an atomless Dedekind complete vector lattice into a Banach space is narrow.
Published
25.12.2015
How to Cite
HumenchukH. I. “On the Sum of Narrow and Finite-Rank Orthogonally Additive Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 12, Dec. 2015, pp. 1620-5, http://umj.imath.kiev.ua/index.php/umj/article/view/2095.
Section
Research articles