Unbounded absolutely weak Dunford-Pettis operators


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ERKURŞUN ÖZCAN N., GEZER N. A. , Zabeti O.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.6, pp.2731-2740, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1904-27
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.2731-2740

Abstract

In the present article, we expose various properties of unbounded absolutely weak Dunford-Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.