The order boundedness of band preserving operators on uniformly complete vector lattices

DOI10.1017/S0305004100063052zbMath0564.47017OpenAlexW2055601423MaRDI QIDQ3678233

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Publication date: 1985

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100063052

zbMATH Keywords

uniformly complete vector latticelocally convex locally solid Hausdorff uniformly complete vector latticenon-order bounded band preserving operator

Mathematics Subject Classification ID

Linear operators on ordered spaces (47B60) Ordered topological linear spaces, vector lattices (46A40)

Related Items (15)

Complex structures on real vector lattices ⋮ Boolean-valued analysis of order-bounded operators ⋮ Invertible disjointness preserving operators ⋮ Boolean methods in positivity ⋮ Derivations on universally complete \(f\)-algebras ⋮ Characterization of hyper-Archimedean vector lattices via disjointness preserving bilinear maps ⋮ Involutions and Complex Structures on Real Vector Lattices ⋮ The inverse of band preserving and disjointness preserving operators ⋮ Representations of Archimedean Riesz spaces by continuous functions ⋮ When the image of a derivation on a uniformly complete \(f\)-algebra is contained in the radical ⋮ Commutativity of some Archimedean ordered algebras. ⋮ The Wickstead problem on Dedekind \(\sigma \)-complete vector lattices ⋮ On band operators ⋮ Order-bounded operators in vector lattices and in spaces of measurable functions ⋮ Inverses and regularity of band preserving operators.

Cites Work

• Order completeness and disjoint completeness of linear partially ordered spaces
• A Note on Disjointness Preserving Operators
• Lateral and Dedekind Completion of Archimedean Lattice Groups
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