Displaying similar documents to “Some results on injective Banach lattices”

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.

On M-operators of q-lattices

Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

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It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.