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WANG Shao-xin, CHEN Zi-li. The Properties of AM-compact OperatorsJ. Journal of Xinyang Normal University (Natural Science Edition), 2007, 20(1): 14-16.
Citation: WANG Shao-xin, CHEN Zi-li. The Properties of AM-compact OperatorsJ. Journal of Xinyang Normal University (Natural Science Edition), 2007, 20(1): 14-16.
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The Properties of AM-compact Operators

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  • The Invariant Subspace Problem is a famous problem in the operator theory.For generalizing the results in Abramovich's paper about the positive compact operators,this paper is devoted to the properties of AM-compact operators on Banach lattice.Its domination and lattice property is given,and it is proven that if a positive operator on a Banach lattice is dominated by an AM-compact operator,then its square is also an AM-compact operator.Some relative properties are also discussed.
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