“Ryll-Nardzewski fixed-point theorem”的意思、由来-开放百科全书

词条

Ryll-Nardzewski fixed-point theorem

释义

Applications
See also
References

In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if is a normed vector space and is a nonempty convex subset of that is compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of has at least one fixed point. (Here, a fixed point of a set of maps is a point that is fixed by each map in the set.)

This theorem was announced by Czesław Ryll-Nardzewski.^[1] Later Namioka and Asplund ^[2] gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.^[3]

Applications

The Ryll-Nardzewski theorem yields the existence of a Haar measure on compact groups.^[4]

References

1. ^{{cite journal|first=C.|last=Ryll-Nardzewski|title=Generalized random ergodic theorems and weakly almost periodic functions|journal=Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.|volume=10|year=1962|pages=271–275}}
2. ^{{cite journal|doi=10.1090/S0002-9904-1967-11779-8|first=I.|last=Namioka|author1-link= Isaac Namioka |author2=Asplund, E. |title=A geometric proof of Ryll-Nardzewski's fixed point theorem|journal=Bull. Amer. Math. Soc.|volume=73|issue=3|year=1967|pages=443–445}}
3. ^{{cite journal|first=C.|last=Ryll-Nardzewski|title=On fixed points of semi-groups of endomorphisms of linear spaces|journal=Proc. 5th Berkeley Symp. Probab. Math. Stat|volume=2: 1|publisher=Univ. California Press|year=1967|pages=55–61}}
4. ^{{cite book|first=N.|last=Bourbaki|title=Espaces vectoriels topologiques. Chapitres 1 à 5|series=Éléments de mathématique.|edition=New|publisher=Masson|location=Paris|year=1981|isbn=2-225-68410-3}}

Andrzej Granas and James Dugundji, Fixed Point Theory (2003) Springer-Verlag, New York, {{isbn|0-387-00173-5}}.
A proof written by J. Lurie

2 : Fixed-point theorems|Theorems in functional analysis

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

Applications

See also

References