Invariant subspace problem for positive L-weakly and M-weakly compact operators


Tonyali C., Bayram E.

TURKISH JOURNAL OF MATHEMATICS, vol.35, no.2, pp.267-273, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.3906/mat-0903-37
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.267-273
  • Keywords: Invariant subspace, L- and M-weakly compact operator, Polynomially L-weakly (M-weakly) compact operator, Dunford-Pettis operator, DUNFORD-PETTIS OPERATORS, BANACH-LATTICES
  • Gazi University Affiliated: Yes

Abstract

In this paper, we show that positive L-weakly and M-weakly compact operators on some real Banach lattices have a non-trivial closed invariant subspace. Also, we prove that any positive L-weakly (or M-weakly) compact operator T : E -> E has a non-trivial closed invariant subspace if there exists a Dunford-Pettis operator S : E -> E satisfying 0 <= T <= S, where E is Banach lattice.