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2007•Journal of Xinyang Normal UniversityRequires access

The Properties of AM-compact Operators

Zili Chen

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Abstract

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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What this paper is about

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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Available abstract

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.

Key concepts: Compact operator, Mathematics, Finite-rank operator, Approximation property, Invariant subspace problem, Lattice (music), Operator (biology), Strictly singular operator

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