Compact-like operators in lattice-nonmed. spaces


Aydin A., Emelyanov E. Y. , Ozcan N. , Marabeh M. A. A.

INDAGATIONES MATHEMATICAE-NEW SERIES, vol.29, no.2, pp.633-656, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1016/j.indag.2017.11.002
  • Title of Journal : INDAGATIONES MATHEMATICAE-NEW SERIES
  • Page Numbers: pp.633-656

Abstract

A linear operator T between two lattice-normed spaces is said to be p-compact if, for any p-bounded net x(alpha),,the net Tx(alpha) has a p-convergent subnet. p-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, AM-compact operators, etc. Similar to M-weakly and L-weakly compact operatois, we define p-M-weakly and p-L-weakly compact operators and study some of their properties. We also study up-continuous and up"compact operators between lattice nonmed vector lattices. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.