Geodesic
Weakly compact-friendly operators
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 27-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMJ_2009_11_2_a3,
     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},
     year = {2009},
     volume = {11},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a3/}
}
TY  - JOUR
AU  - M. Çağlar
AU  - T. Mısırlıoğlu
TI  - Weakly compact-friendly operators
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2009
SP  - 27
EP  - 30
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a3/
LA  - en
ID  - VMJ_2009_11_2_a3
ER  - 
%0 Journal Article
%A M. Çağlar
%A T. Mısırlıoğlu
%T Weakly compact-friendly operators
%J Vladikavkazskij matematičeskij žurnal
%D 2009
%P 27-30
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a3/
%G en
%F VMJ_2009_11_2_a3
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/

[1] Abramovich Y. A., Aliprantis C. D., An Invitation to Operator Theory, Graduate Studies in Mathematics, 50, Amer. Math. Soc., Providence, Rhode Island, 2002 | MR | Zbl

[2] Abramovich Y. A., Aliprantis C. D., Burkinshaw O., “The invariant subspace problem: some recent advances”, Workshop on Measure Theory and Real Analysis (Grado, 1995) ; Rend. Inst. Mat. Univ. Trieste, 29 (1998), 3–79 | MR | Zbl

[3] Aliprantis C. D., Burkinshaw O., Positive Operators, Springer, The Netherlands, 2006, 376 pp. | MR

[4] Hoover T. B., “Quasi-similarity of operators”, Illinois J. Math., 16 (1972), 678–686 | MR | Zbl

[5] Laursen K. B., Neumann M. M., An Introduction to local spectral theory, London Mathematical Society Monographs. New ser., 20, Clarendon Press, Oxford, 2000, 577 pp. | MR | Zbl

[6] Sz.-Nagy B., Foiaş C., Harmonic analysis of operators on Hilbert space, American Elsevier Publishing Company, Inc., New York, 1970, 389 pp. | MR