Displaying similar documents to “On isomorphisms and hyper-reflexivity of closed subspace lattices.”

Reflexivity of bilattices

Kamila Kliś-Garlicka (2013)

Czechoslovak Mathematical Journal

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We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice ℒ we may associate a bilattice Σ ℒ . Similarly, having a bilattice Σ we may construct a subspace lattice ℒ Σ . Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.

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 subobject lattices and reflexive endomorphism algebras

Dong Sheng Zhao (2003)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.