Partially ordered vector space, ordered as a lattice
"Vector lattice" redirects here. For other uses, see Lattice (disambiguation).
In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice.
Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper Sur la décomposition des opérations fonctionelles linéaires.
Riesz spaces have wide-ranging applications. They are important in measure theory, in that important results are special cases of results for Riesz spaces. For example, the Radon–Nikodym theorem follows as a special case of the Freudenthal spectral theorem. Riesz spaces have also seen application in mathematical economics through the work of Greek-American economist and mathematician Charalambos D. Aliprantis.
Rieszspace, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Rieszspaces are...
Proximity space Rising sun lemma Denjoy–Riesz theorem F. and M. Riesz theorem Riesz representation theorem Riesz-Fischer theorem Riesz groups Riesz's lemma...
The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes...
by Frigyes Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of...
Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study...
real space R n {\displaystyle \mathbf {R} ^{n}} can be ordered by comparing its vectors componentwise. Ordered vector spaces, for example Rieszspaces, are...
mathematics, the Riesz potential is a potential named after its discoverer, the Hungarian mathematician Marcel Riesz. In a sense, the Riesz potential defines...
Hardy space Hilbert space Hölder space LF-space Lp space Minkowski space Montel space Morrey–Campanato space Orlicz spaceRieszspace Schwartz space Sobolev...
(1907) and Riesz (1907). The general result, that the dual of a Hilbert space is identified with the Hilbert space itself, can be found in Riesz (1934)....
result in Rieszspace theory proved by Hans Freudenthal in 1936. It roughly states that any element dominated by a positive element in a Rieszspace with the...
A.} An ordered vector space is called order complete, Dedekind complete, a complete vector lattice, or a complete Rieszspace, if it is order complete...
setsPages displaying short descriptions of redirect targets Rieszspace – Partially ordered vector space, ordered as a lattice Lam (2005) p. 289 Lam (2005) p...
Marcel Riesz (Hungarian: Riesz Marcell [ˈriːs ˈmɒrt͡sɛll]; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation...
(possibly infinitely many) such open intervals and rays. A topological space X is called orderable or linearly orderable if there exists a total order...
spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz...
13 (Second ed.). New York: Springer-Verlag. p. 356. ISBN 0-387-00444-0. Riesz, Frigyes & Béla Szőkefalvi-Nagy (1990). Functional Analysis. Courier Dover...
uniformly convex Banach space is reflexive, while the converse is not true. Every uniformly convex Banach space is a Radon–Rieszspace, that is, if { f n }...
finite-dimensional; this is a consequence of Riesz's lemma. (In fact, a more general result is true: a topological vector space is locally compact if and only if...
an Alexandrov topology is known as an Alexandrov-discrete space or finitely generated space. Alexandrov topologies are uniquely determined by their specialization...
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