The Projection onto the Center of Operators in a Banach Lattice.
Jürgen Voigt (1988)
Mathematische Zeitschrift
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Jürgen Voigt (1988)
Mathematische Zeitschrift
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C. B. Huijsmans, B. de Pagter (1991)
Compositio Mathematica
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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.
Beatriz Porras Pomares (1986)
Extracta Mathematicae
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Singh, R.K. (2005)
International Journal of Mathematics and Mathematical Sciences
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A.W. Wickstead (1991)
Mathematische Zeitschrift
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J. Szulga (1979)
Colloquium Mathematicae
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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.
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...
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...
Belmesnaoui Aqzzouz, Redouane Nouira (2009)
Czechoslovak Mathematical Journal
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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 into a Banach lattice is an order -complete vector lattice.