Weakly compact-friendly operators
Автор: Caglar Mert, Misirliouglu Tunc
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.11, 2009 года.
Бесплатный доступ
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.
Invariant subspace, positive operator, weakly compact-friendly, locally quasi-nilpotent
Короткий адрес: https://sciup.org/14318269
IDR: 14318269
Список литературы Weakly compact-friendly operators
- Abramovich Y. A., Aliprantis C. D. An Invitation to Operator Theory//Amer. Math. Soc.-Rhode Island: Providence, 2002.-Vol. 50 (Graduate Studies in Mathematics).
- 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.-1998.-Vol. 29.-P. 3-79.
- Aliprantis C. D., Burkinshaw O. Positive operators.-The Netherlands: Springer, 2006.-376 p.
- Hoover T. B. Quasi-similarity of operators//Illinois J. Math.-1972.-Vol. 16.-P. 678-686.
- Laursen K. B., Neumann M. M. An Introduction to local spectral theory. London Mathematical Society Monographs. New ser. 20.-Oxford: Clarendon Press, 2000.-577 p.
- Sz.-Nagy B., Foias C. Harmonic analysis of operators on Hilbert space.-New York: American Elsevier Publishing Company, Inc., 1970.-389 p.
Статья научная