The minimum principle for affine functions and isomorphisms of continuous affine function spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419890" target="_blank" >RIV/00216208:11320/20:10419890 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=C7Q7D2LmM9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=C7Q7D2LmM9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00013-019-01371-0" target="_blank" >10.1007/s00013-019-01371-0</a>

Result language
angličtina
Original language name
The minimum principle for affine functions and isomorphisms of continuous affine function spaces
Original language description
Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that if f : X -> R is an affine function with the point of continuity property such that f <= 0 on ext X, then f <= 0 on X. As a corollary of this minimum principle, we obtain a generalization of a theorem by C.H. Chu and H.B. Cohen by proving the following result. Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and let T : Ac(X). Ac(Y) be an isomorphism such that parallel to T parallel to . parallel to T-1 parallel to < 2. Then ext X is homeomorphic to ext Y.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-00941S" target="_blank" >GA17-00941S: Topological and geometrical properties of Banach spaces and operator algebras II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)