Chapter 35: Riesz spaces
351
Partially ordered linear spaces
Partially ordered linear spaces; positive cones; suprema and
infima; positive linear operators; order-continuous linear
operators; Riesz homomorphisms; quotient spaces; reduced powers;
representation of p.o.l.ss as subspaces of reduced powers of
R; Archimedean spaces.
352
Riesz spaces
Riesz spaces; identities; general distributive laws; Riesz
homomorphisms; Riesz subspaces; order-dense subspaces and
order-continuous operators; bands; the algebra of complemented
bands; the algebra of projection bands; principal bands;
f-algebras.
353
Archimedean and Dedekind complete Riesz spaces
Order-dense subspaces; bands; Dedekind (σ)-complete spaces;
order-closed Riesz subspaces; order units; f-algebras.
354
Banach lattices
Riesz norms; Fatou norms; the Levi property; order-continuous
norms; order-unit norms; M-spaces; are isomorphic to C(X) for
compact Hausdorff X; L-spaces; uniform integrability in
L-spaces.
355
Spaces of linear operators
Order-bounded linear operators; the space L~(U;V);
order-continuous operators; extension of order-continuous operators;
the space L×(U,V); order-continuous norms.
356
Dual spaces
The spaces U~, U×, U*; biduals, embeddings
U→V× where VÍU~; perfect Riesz
spaces; L- and M-spaces; uniformly integrable sets in the dual
of an M-space; relative weak compactness in L-spaces.
TeX,
PDF,
ro-PDF (results-only version).
Return to contents page.