Çağlar, MertMısırlıoğlu, Remzi Tunç2016-08-312016-08-312011-091385-1292http://hdl.handle.net/11413/1374Let 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.en-USinvariant subspacepositive operatorcompact-friendlylocally quasi-nilpotentpositive quasi-similaritystrongly compact-friendlyoperatorsdeğişmeyen alt uzaypozitif operatörkompakt dostulokal yarı-nilpotentpozitif yarı-benzerlikgüçlü kompakt dostuoperatörlerArticle2945030000092945030000092-s2.0-800522635402-s2.0-80052263540