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Banach格上正则b-AM-紧算子空间的AM-空间

, PP. 362-364

Keywords: Banach格,b-AM-紧算子,AL-空间,AM-空间

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Abstract:

首先讨论了Banach格上的b-AM-紧算子的模的存在性,即Banach格到AM-空间上的b-AM-紧算子的模存在,且其模也是b-AM-紧算子.其次,讨论了在正则b-AM-紧算子空间中,若b-AM-紧算子序列{Tn}依b-AM-范数收敛于T,且Tn在Krb-AM(E,F)的模|Tn|存在,T在Krb-AM(E,F)的模|T|存在,即得到如下结果如果‖Tn-T‖b-AM0,且Tn在Krb-AM(E,F)的模|Tn|存在,则T在Krb-AM(E,F)的模|T|存在,且满足‖|Tn|-|T|‖b-AM0.最后给出Banach格上所有从E到F的正则b-AM-紧算子空间在‖·‖b-AM-范数下是AM-空间当且仅当E是AL-空间且F是AM-空间的结果.

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