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Freudenthal spectral theorem information


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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Freudenthal spectral theorem

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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...

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Freudenthal

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Freudenthal, asteroid Bruntál, town in the Czech Republic, known in German as Freudenthal Freudenthal spectral theorem Freudenthal suspension theorem...

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Hans Freudenthal

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minimal surfaces. In 1936, while working with Brouwer, Freudenthal proved the Freudenthal spectral theorem on the existence of uniform approximations by simple...

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Riesz space

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spaces. For example, the Radon–Nikodym theorem follows as a special case of the Freudenthal spectral theorem. Riesz spaces have also seen application...

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Signed measure

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lattice and in so doing the Radon–Nikodym theorem can be shown to be a special case of the Freudenthal spectral theorem. If X is a compact separable space,...

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Algebraic topology

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theorem Freudenthal suspension theorem Hurewicz theorem Künneth theorem Lefschetz fixed-point theorem Leray–Hirsch theorem Poincaré duality theorem Seifert–van...

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List of theorems

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Bauer–Fike theorem (spectral theory) Bayes' theorem (probability) Beatty's theorem (Diophantine approximation) Beauville–Laszlo theorem (vector bundles)...

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EHP spectral sequence

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University Press, ISBN 0-691-09586-8 Whitehead, George W. (1953), "On the Freudenthal theorems", Annals of Mathematics, Second Series, 57 (2): 209–228, doi:10.2307/1969855...

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Stable homotopy theory

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applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space X {\displaystyle...

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Homotopy groups of spheres

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hold for larger dimensions. The first such result was Hans Freudenthal's suspension theorem, published in 1937. Stable algebraic topology flourished between...

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September 1905

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communication with extraterrestrial intelligence and for the Freudenthal spectral theorem; in Luckenwalde, Prussia (d. 1990) Arsenio Cruz Herrera, the...

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Heinz Hopf

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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...

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Homotopy group

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Blakers–Massey theorem, also known as excision for homotopy groups. Freudenthal suspension theorem, a corollary of excision for homotopy groups. There is also...

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Zonal spherical function

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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...

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Symmetric cone

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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...

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Hans Duistermaat

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defense, so the official supervision was taken over by geometer Hans Freudenthal. After a postdoctoral stay in Lund (1969–70), Duistermaat returned to...

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Glossary of algebraic topology

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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...

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Postnikov system

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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...

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Timeline of manifolds

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Walter de Gruyter. p. 43. ISBN 9783110961164. Retrieved 15 June 2018. Freudenthal, Hans (2014-05-12). L. E. J. Brouwer Collected Works: Geometry, Analysis...

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Complex projective space

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homotopy theory (which can be done with the Serre spectral sequence, Freudenthal suspension theorem, and the Postnikov tower). The map comes from the...

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Group cohomology

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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...

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