Regularity of Banach lattice valued martingales

J. Szulga

Displaying similar documents to “Regularity of Banach lattice valued martingales”

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.

Biduals of p-lattice summing operators.

Beatriz Porras Pomares (1986)

Extracta Mathematicae

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$ℒ_{π}$ -Spaces and cone summing operators

P. Mangheni (1988)

Studia Mathematica

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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...

The Projection onto the Center of Operators in a Banach Lattice.

Jürgen Voigt (1988)

Mathematische Zeitschrift

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The lattice-isometric copies of $ℓ_{\infty} (Γ)$ in quotients of Banach lattices.

Wójtowicz, Marek (2003)

International Journal of Mathematics and Mathematical Sciences

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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.

A local characterization of Banach lattices with order continuous norm

S. Bernau, H. Lacey (1976)

Studia Mathematica

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Narrow operators on lattice-normed spaces

Marat Pliev (2011)

Open Mathematics

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The aim of this article is to extend results of Maslyuchenko, Mykhaylyuk and Popov about narrow operators on vector lattices. We give a new definition of a narrow operator, where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator...

Little G. T. for lp-lattice summing operators

Mezrag, Lahcène (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B28, 47D15. In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.

A disjointness type property of conditional expectation operators

Beata Randrianantoanina (2005)

Colloquium Mathematicae

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We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.