Displaying similar documents to “The Projection onto the Center of Operators in a Banach Lattice.”

About the class of ordered limited operators

A. El Kaddouri, Mohammed Moussa (2013)

Acta Universitatis Carolinae. Mathematica et Physica

Similarity:

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

A disjointness type property of conditional expectation operators

Beata Randrianantoanina (2005)

Colloquium Mathematicae

Similarity:

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.

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

Niels Jakob Laustsen, Richard J. Loy (2005)

Banach Center Publications

Similarity:

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...

Little G. T. for lp-lattice summing operators

Mezrag, Lahcène (2006)

Serdica Mathematical Journal

Similarity:

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.

The order σ -complete vector lattice of AM-compact operators

Belmesnaoui Aqzzouz, Redouane Nouira (2009)

Czechoslovak Mathematical Journal

Similarity:

We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice E into a Banach lattice F is an order σ -complete vector lattice.