Closed ideals in the Banach algebra of operators on a Banach space

Niels Jakob Laustsen; Richard J. Loy

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Displaying similar documents to “Closed ideals in the Banach algebra of operators on a Banach space”

Biduals of p-lattice summing operators.

Beatriz Porras Pomares (1986)

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About the class of ordered limited operators

A. El Kaddouri, Mohammed Moussa (2013)

Acta Universitatis Carolinae. Mathematica et Physica

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We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.

The $b$ -weak compactness of weak Banach-Saks operators

Belmesnaoui Aqzzouz, Othman Aboutafail, Taib Belghiti, Jawad H'michane (2013)

Mathematica Bohemica

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We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.

The lattice copies of $ℓ_{1}$ in Banach lattices

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

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It is known that a Banach lattice with order continuous norm contains a copy of $ℓ_{1}$ if and only if it contains a lattice copy of $ℓ_{1}$ . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_{0}$ - and $ℓ_{\infty}$ -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.

Regularity of Banach lattice valued martingales

J. Szulga (1979)

Colloquium Mathematicae

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Domination by positive Banach-Saks operators

Julio Flores, César Ruiz (2006)

Studia Mathematica

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Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.

Properties of modulus of monotonicity and Opial property in direct sums

Joanna Markowicz, Stanisław Prus (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing to general direct sums of Banach spaces are established.

Maximal left ideals of the Banach algebra of bounded operators on a Banach space

H. G. Dales, Tomasz Kania, Tomasz Kochanek, Piotr Koszmider, Niels Jakob Laustsen (2013)

Studia Mathematica

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Factorization and domination of positive Banach-Saks operators

Julio Flores, Pedro Tradacete (2008)

Studia Mathematica

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It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.

Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (Xv) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(Xv) is equal to the supremum of such deviations attained on the coordinates Xv. This is a quantitative version for operators of...