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On The Properties Of Special Operators On Banach Lattice

Posted on:2014-01-30Degree:MasterType:Thesis
Country:ChinaCandidate:Y F CongFull Text:PDF
GTID:2230330398475033Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
In this paper, we deduce the domination property, lattice order property and duality property of the O-Dunford-Pettis operators on Banach lattices. And we obtain some relationships between the O-Dunford-Pettis operators and other operators.First, we give some sufficient conditions for that an operator dominated by a O-Dunford-Pettis operator is again an O-Dunford-Pettis. And we prove that an operator dominated by other operators such as Dunford-Pettis operator is an O-Dunford-Pettis operator subject to some conditions. In addition we show the existence of the modulus of O-Dunford-Pettis operators. We also present some sufficient conditions under which the modulus an O-Dunford-Pettis operator is again an O-Dunford-Pettis operator. And if the modulu of an operator is O-Dunford-Pettis, we show the operator itself is an O-Dunford-Pettis under some conditions.Then, we give some sufficient conditions for that an O-Dunford-Pettis operator admits a dual operator which is also O-Dunford-Pettis. And we prove that if the dual operator of an operator is O-Dunford-Pettis, the operator itself is also O-Dunford-Pettis under some conditions.At last we obtain some relationships between the O-Dunford-Pettis operators and other operators such as AM-compact operators and Dunford-Pettis operators.
Keywords/Search Tags:Banach lattice, O-Dunford-Pettis operator, modulus, duality operator
PDF Full Text Request
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