Displaying similar documents to “Reflexivity of bilattices”

J-subspace lattices and subspace M-bases

W. Longstaff, Oreste Panaia (2000)

Studia Mathematica

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The class of J-lattices was defined in the second author’s thesis. A subspace lattice on a Banach space X which is also a J-lattice is called a J- subspace lattice, abbreviated JSL. Every atomic Boolean subspace lattice, abbreviated ABSL, is a JSL. Any commutative JSL on Hilbert space, as well as any JSL on finite-dimensional space, is an ABSL. For any JSL ℒ both LatAlg ℒ and ℒ ⊥ (on reflexive space) are JSL’s. Those families of subspaces which arise as the set of atoms of some JSL on...

On reflexive closed set lattices

Zhongqiang Yang, Dong Sheng Zhao (2010)

Commentationes Mathematicae Universitatis Carolinae

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For a topological space X , let S ( X ) denote the set of all closed subsets in X , and let C ( X ) denote the set of all continuous maps f : X → X . A family 𝒜 ⊆ S ( X ) is called reflexive if there exists 𝒞 ⊆ C ( X ) such that 𝒜 = { A ∈ S ( X ) : f ( A ) ⊆ A for every f ∈ 𝒞 } . Every reflexive family of closed sets in space X forms a sub complete lattice of the lattice of all closed sets in X . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families...

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.