Geodesic
Weakly compact-friendly operators
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 27-30

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We introduce weak compact-friendliness as an extension of compact-friendliness, and and prove that if a non-zero weakly compact-friendly operator $B\colon E\to E$ 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. 
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     author = {M. \c{C}a\u{g}lar and T. M{\i}s{\i}rl{\i}o\u{g}lu},
     title = {Weakly compact-friendly operators},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {27--30},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a3/}
}
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M. Çağlar; T. Mısırlıoğlu. Weakly compact-friendly operators. Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 27-30. http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a3/