Some results on b-AM-compact operators |
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Authors: | Na Cheng |
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Institution: | 1. School of Science, Xihua University, Chengdu Sichuan 610031, P.R. Chinachengnaanna@126.com |
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Abstract: | We show that for positive operator B : E → E on Banach lattices, if there exists a positive operator S : E → E such that:1.SB ≤ BS;2.S is quasinilpotent at some x0 > 0; 3.S dominates a non-zero b-AM-compact operator, then B has a non-trivial closed invariant subspace. Also, we prove that for two commuting non-zero positive operators on Banach lattices, if one of them is quasinilpotent at a non-zero positive vector and the other dominates a non-zero b-AM-compact operator, then both of them have a common non-trivial closed invariant ideal. Then we introduce the class of b-AM-compact-friendly operators and show that a non-zero positive b-AM- compact-friendly operator which is quasinilpotent at some x0 > 0 has a non-trivial closed invariant ideal. |
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Keywords: | 47A15 47B60 47B65 46B42 |
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