设P表示可膨胀、σ-可膨胀、离散可膨胀、σ-离散可膨胀这四种性质之一.本文主要证明:(1)设X=lim{Xα,παβ,∧}并且每个投射πα是开满映射,如果X是|∧|-仿紧(遗传|∧|-仿紧)的,并且每个Xα都具有性质P(遗传性质P),则X具有性质P(遗传...设P表示可膨胀、σ-可膨胀、离散可膨胀、σ-离散可膨胀这四种性质之一.本文主要证明:(1)设X=lim{Xα,παβ,∧}并且每个投射πα是开满映射,如果X是|∧|-仿紧(遗传|∧|-仿紧)的,并且每个Xα都具有性质P(遗传性质P),则X具有性质P(遗传性质P);(2)如果X=multiply from σ∈∑ Xσ是|∑|-仿紧(遗传|∑|-仿紧)空间,则具有性质P(遗传性质p)当且仅当(?)F∈[∑]<ω,multiply from σ∈∑ Xσ具有性质P(遗传性质P).展开更多
For M-matrix equations, we provide a necessary and sufficient condition for that the solution of the equations has the property p, which improves and generalizes the corresponding results of [1] and [2].
Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the p...The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.展开更多
文摘设P表示可膨胀、σ-可膨胀、离散可膨胀、σ-离散可膨胀这四种性质之一.本文主要证明:(1)设X=lim{Xα,παβ,∧}并且每个投射πα是开满映射,如果X是|∧|-仿紧(遗传|∧|-仿紧)的,并且每个Xα都具有性质P(遗传性质P),则X具有性质P(遗传性质P);(2)如果X=multiply from σ∈∑ Xσ是|∑|-仿紧(遗传|∑|-仿紧)空间,则具有性质P(遗传性质p)当且仅当(?)F∈[∑]<ω,multiply from σ∈∑ Xσ具有性质P(遗传性质P).
文摘For M-matrix equations, we provide a necessary and sufficient condition for that the solution of the equations has the property p, which improves and generalizes the corresponding results of [1] and [2].
文摘Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
基金Supported by the National Research Foundation of South Africa(Grant Nos.85619 and 101265)
文摘The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.
