Weakly Compact-Friendly Operators - Çağlar, Mert; Mısırlıoğlu, Remzi Tunç (Institution Of Russian Academy Of Sciences South Mathematical İnstitute Of Vladikavkaz Scientific Center Of The Russian Academy Of Sciences And The Government Of Republic Of North Ossetia-Alania, 22, Markusa Street, Vladikavkaz, 362027, 2009)
We introduce weak compact-friendliness as an extension of compact-friendliness, and and prove that if a non-zero weakly compact-friendly operator B: E→ E on a Banach lattice is quasi-nilpotent at some non-zero positive vector, then B has a non-trivial closed invariant ideal. Relevant facts related to compact-friendliness are also discussed.
Keywords: Invariant subspace; positive operator; weakly compact-friendly; locally quasi-nilpotent; Değişmeyen alt uzay; pozitif operatör; zayıf kompakt dostu; lokal yarı-nilpotent