Displaying similar documents to “Properties of modulus of monotonicity and Opial property in direct sums”

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

Niels Jakob Laustsen, Richard J. Loy (2005)

Banach Center Publications

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In general, little is known about the lattice of closed ideals in the Banach algebra ℬ(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in ℬ(F), where F is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice...

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.

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...

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 ∞ -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.