Riesz space

Riesz space

Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices

Published in Hemen Dutta, Topics in Contemporary Mathematical Analysis and Applications, 2020

A subset A of a vector lattice is called solid whenever |x| ≤ |y| and y ∈ A imply x ∈ A. A solid vector subspace is referred to as an order ideal. An order closed ideal is referred to as a band. A sublattice Y of a vector lattice is majorizing E if, for every x ∈ E, there exists y ∈ Y with x ≤ y; see, for example, [1–3,32]. Let E be a vector lattice and τ be a linear topology on E that has a base at zero consisting of solid sets. Then, the pair (E,τ) is said to be a locally solid vector lattice (or, locally solid Riesz space).

Semicontinuity of the minimal solution mappings to parametric set optimization problems on Banach lattices

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Journal Information

Published in Optimization, 2023

Yu Han, Kai Zhang

Let be a Riesz space. is said to be a normed Riesz space, if E is a normed linear space, whose norm is a compatible with the partial order in the sense that holds for any with .a Banach lattice, if is an normed Riesz space which is complete with respect to the norm.

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Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices

Semicontinuity of the minimal solution mappings to parametric set optimization problems on Banach lattices