Abstract reflexive sublattices and completely distributive collapsibility

DOI10.1017/S0004972700032226zbMath0920.47005MaRDI QIDQ4224795

J. B. Nation, Oreste Panaia, William Ellison Longstaff

Publication date: 16 September 1999

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Galois connectionoperator algebrasreflexivesubspace latticescompletely distributiveleast complete congruence

Mathematics Subject Classification ID

Complete distributivity (06D10) Abstract operator algebras on Hilbert spaces (47L30) Invariant subspaces of linear operators (47A15) Representation theory of lattices (06B15) Linear operators in algebras (47C05)

Related Items (12)

Lie isomorphisms of reflexive algebras. II. ⋮ Jordan isomorphisms of \(\mathcal J\)-subspace lattice algebras ⋮ Invertibility preserving linear maps on \(\mathcal J\)-subspace lattice algebras ⋮ Jordan elementary operators on \(\mathcal J\)-subspace lattice algebras ⋮ Lie triple derivations on \(\mathcal{J}\)-subspace lattice algebras ⋮ Rank-one operators in reflexive one-sided \(\mathcal A\)-submodules ⋮ Additive maps derivable at some points on \(\mathcal J\)-subspace lattice algebras ⋮ Algebraic isomorphisms and $\mathcal {J}$-subspace lattices ⋮ Centralizers of \(\mathcal J\)-subspace lattice algebras ⋮ REFLEXIVE INDEX OF A FAMILY OF SUBSPACES ⋮ Full-derivable points of \(\mathcal {J}\)-subspace lattice algebras ⋮ Lie derivations of $\mathcal J$-subspace lattice algebras

Cites Work

• Tight Galois Connections and Complete Distributivity
• Covers in Free Lattices
• Semisimplicity in Operator Algebras and Subspace Lattices
• Strongly Reflexive Lattices
• On Two Questions of Halmos Concerning Subspace Lattices
• Reflexive Lattices of Subspaces
• Completely Distributive Complete Lattices

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