In mathematics, the Freudenthal spectral theorem is a result in Riesz space theory proved by Hans Freudenthal in 1936. It roughly states that any element dominated by a positive element in a Riesz space with the principal projection property can in a sense be approximated uniformly by simple functions.
Numerous well-known results may be derived from the Freudenthal spectral theorem. The well-known Radon–Nikodym theorem, the validity of the Poisson formula and the spectral theorem from the theory of normal operators can all be shown to follow as special cases of the Freudenthal spectral theorem.
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In mathematics, the Freudenthalspectraltheorem is a result in Riesz space theory proved by Hans Freudenthal in 1936. It roughly states that any element...
minimal surfaces. In 1936, while working with Brouwer, Freudenthal proved the Freudenthalspectraltheorem on the existence of uniform approximations by simple...
lattice and in so doing the Radon–Nikodym theorem can be shown to be a special case of the Freudenthalspectraltheorem. If X is a compact separable space,...
University Press, ISBN 0-691-09586-8 Whitehead, George W. (1953), "On the Freudenthaltheorems", Annals of Mathematics, Second Series, 57 (2): 209–228, doi:10.2307/1969855...
applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space X {\displaystyle...
hold for larger dimensions. The first such result was Hans Freudenthal's suspension theorem, published in 1937. Stable algebraic topology flourished between...
communication with extraterrestrial intelligence and for the Freudenthalspectraltheorem; in Luckenwalde, Prussia (d. 1990) Arsenio Cruz Herrera, the...
to the Euler characteristic of the manifold. This theorem is now called the Poincaré–Hopf theorem. Hopf spent the year after his doctorate at the University...
Blakers–Massey theorem, also known as excision for homotopy groups. Freudenthal suspension theorem, a corollary of excision for homotopy groups. There is also...
Laplacian on G, a proof formally parallel to Helgason's reworking of Freudenthal's classical proof of the Weyl character formula, using the radial component...
0. There is a later more direct proof using the Freudenthal diagonalization theorem due to Freudenthal (1951): he proved that given any matrix in the algebra...
defense, so the official supervision was taken over by geometer Hans Freudenthal. After a postdoctoral stay in Lund (1969–70), Duistermaat returned to...
to the base point of X). Freudenthal suspension theorem For a nondegenerately based space X, the Freudenthal suspension theorem says: if X is (n-1)-connected...
coefficient theorem giving π 4 ( S 3 ) = Z / 2 {\displaystyle \pi _{4}\left(S^{3}\right)=\mathbb {Z} /2} . Moreover, because of the Freudenthal suspension...
Walter de Gruyter. p. 43. ISBN 9783110961164. Retrieved 15 June 2018. Freudenthal, Hans (2014-05-12). L. E. J. Brouwer Collected Works: Geometry, Analysis...
homotopy theory (which can be done with the Serre spectral sequence, Freudenthal suspension theorem, and the Postnikov tower). The map comes from the...
Lyndon–Hochschild–Serre spectral sequence. The cohomology groups Hn(G, M) of finite groups G are all torsion for all n≥1. Indeed, by Maschke's theorem the category...