A note on a problem of Abramovich, Aliprantis and Burkinshaw

ÇAĞLAR M., Misirlioglu T.

POSITIVITY, cilt.15, sa.3, ss.473-480, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1007/s11117-010-0096-2
  • Dergi Adı: POSITIVITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.473-480
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

Let B and T be two positive operators on a Banach lattice such that B is compact-friendly and T is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that T has a non-trivial closed invariant subspace provided B is positively quasi-similar to T. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed.