The Experts below are selected from a list of 1422 Experts worldwide ranked by ideXlab platform
Dirk Werner - One of the best experts on this subject based on the ideXlab platform.
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banach spaces with the daugavet property
1999Co-Authors: Vladimir Kadets, Roman Shvidkoy, Gleb Sirotkin, Dirk WernerAbstract:A Banach space X is said to have the Daugavet property if every Operator T: X -* X of rank 1 satisfies 11 Id +Tl= 1 + flTIl. We show that then every Weakly Compact Operator satisfies this equation as well and that X contains a copy of t1. However, X need not contain a copy of L1. We also study pairs of spaces X C Y and Operators T: X -* Y satisfying I I J + T I I -_ 1-4- 1f T I I, where J: X -* Y is the natural embedding. This leads to the result that a Banach space with the Daugavet property does not embed into a space with an unconditional basis. In another direction, we investigate spaces where the set of Operators with f Id +Tll 1 + Il T l I is as small as possible and give characterisations in terms of a smoothness condition.
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banach spaces with the daugavet property
1997Co-Authors: Vladimir Kadets, Roman Shvidkoy, Gleb Sirotkin, Dirk WernerAbstract:A Banach space $X$ is said to have the Daugavet property if every Operator $T: X\to X$ of rank~$1$ satisfies $\|Id+T\| = 1+\|T\|$. We show that then every Weakly Compact Operator satisfies this equation as well and that $X$ contains a copy of $\ell_{1}$. However, $X$ need not contain a copy of $L_{1}$. We also study pairs of spaces $X\subset Y$ and Operators $T: X\to Y$ satisfying $\|J+T\|=1+\|T\|$, where $J: X\to Y$ is the natural embedding. This leads to the result that a Banach space with the Daugavet property does not embed into a space with an unconditional basis. In another direction, we investigate spaces where the set of Operators with $\|Id+T\|=1+\|T\|$ is as small as possible and give characterisations in terms of a smoothness condition.
Mohamed Hajji - One of the best experts on this subject based on the ideXlab platform.
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domination problem on banach lattices and almost weak Compactness
2015Co-Authors: Hamadi Baklouti, Mohamed HajjiAbstract:In this paper we give several new results concerning domination problem in the setting of positive Operators between Banach lattices. Mainly, it is proved that every positive Operator \(R\) on a Banach lattice \(E\) dominated by an almost Weakly Compact Operator \(T\) satisfies that the \(R^2\) is almost Weakly Compact. Domination by strictly singular Operators is also considered. Moreover, we present some interesting connections between strictly singular, disjointly strictly singular and almost Weakly Compact Operators.
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domination problem on banach lattices and almost weak Compactness
2015Co-Authors: Hamadi Baklouti, Mohamed HajjiAbstract:In this paper we give several new results concerning domination problem in the setting of positive Operators between Banach lattices. Mainly, it is proved that every positive Operator \(R\) on a Banach lattice \(E\) dominated by an almost Weakly Compact Operator \(T\) satisfies that the \(R^2\) is almost Weakly Compact. Domination by strictly singular Operators is also considered. Moreover, we present some interesting connections between strictly singular, disjointly strictly singular and almost Weakly Compact Operators.
Birol Altın - One of the best experts on this subject based on the ideXlab platform.
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the relation between b Weakly Compact Operator and kb Operator
2019Co-Authors: Bahri Turan, Birol AltınAbstract:Our aim is to solve the problem asked by Bahramnezhad and Azar in "KB-Operators on Banach lattices and their relationships with Dunford-Pettis and order Weakly Compact Operators". We show that a continuous Operators R from a Banach lattice N into a Banach space M is a b-Weakly Compact Operator if and only if R is a KB-Operator.
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ON b-Weakly Compact OperatorS ON BANACH LATTICES
2007Co-Authors: Birol AltınAbstract:In this paper every b-Weakly Compact Operator is shown to factor through a KB-space. Also we give some necessary and sufficient conditions for a continuous Operator T : E → X from a Banach lattice into a Banach space to be a b-Weakly Compact. Moreover, we investigated the order structure of b-Weakly Compact Operator.
Omid Zabeti - One of the best experts on this subject based on the ideXlab platform.
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dunford pettis and Compact Operators based on unbounded absolute weak convergence
2017Co-Authors: Nazife Erkursun Ozcan, Niyazi Anil Gezer, Omid ZabetiAbstract:In this paper, using the concept of unbounded absolute weak convergence ($uaw$-convergence, for short) in a Banach lattice, we define two classes of continuous Operators, named $uaw$-Dunford-Pettis and $uaw$-Compact Operators. We investigate some properties and relations between them. In particular, we consider some hypotheses on domain or range spaces of Operators such that the adjoint or the modulus of a $uaw$-Dunford-Pettis or $uaw$-Compact Operator inherits a similar property. In addition, we look into some connections between Compact Operators, Weakly Compact Operators, and Dunford-Pettis ones with $uaw$-versions of these Operators. Moreover, we examine some relations between $uaw$-Dunford-Pettis Operators, $M$-Weakly Compact Operators, $L$-Weakly Compact Operators, and $o$-Weakly Compact ones. As a significant outcome, we show that the square of any positive $uaw$-Dunford-Pettis ($M$-Weakly Compact) Operator on an order continuous Banach lattice is Compact. Many examples are given to illustrate the essential conditions, as well.
Zabeti Omid - One of the best experts on this subject based on the ideXlab platform.
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Dunford-Pettis and Compact Operators Based on Unbounded Absolute Weak Convergence
2019Co-Authors: Ozcan, Nazife Erkursun, Gezer, Niyazi Anil, Zabeti OmidAbstract:In this paper, using the concept of unbounded absolute weak convergence ($uaw$-convergence, for short) in a Banach lattice, we define two classes of continuous Operators, named $uaw$-Dunford-Pettis and $uaw$-Compact Operators. We investigate some properties and relations between them. In particular, we consider some hypotheses on domain or range spaces of Operators such that the adjoint or the modulus of a $uaw$-Dunford-Pettis or $uaw$-Compact Operator inherits a similar property. In addition, we look into some connections between Compact Operators, Weakly Compact Operators, and Dunford-Pettis ones with $uaw$-versions of these Operators. Moreover, we examine some relations between $uaw$-Dunford-Pettis Operators, $M$-Weakly Compact Operators, $L$-Weakly Compact Operators, and $o$-Weakly Compact ones. As a significant outcome, we show that the square of any positive $uaw$-Dunford-Pettis ($M$-Weakly Compact) Operator on an order continuous Banach lattice is Compact. Many examples are given to illustrate the essential conditions, as well.Comment: 9 pages. There is no major difference with the previous version (21 Dec 2018), just a few statements have been added and restated. The title has changed to be more effective. Submitted to the journa
