- Example
- See also
- References
In mathematics, a Dirichlet algebra is a particular type of algebra associated to a compact Hausdorff space X. It is a closed subalgebra of C(X), the uniform algebra of bounded continuous functions on X, whose real parts are dense in the algebra of bounded continuous real functions on X. The concept was introduced by {{harvs|first=Andrew|last=Gleason|authorlink=Andrew Gleason|year=1957|txt}}.
Example
Let 
be the set of all rational functions that are continuous on 
; in other words functions that have no poles in . Then
is a *-subalgebra of 
, and of 
. If 
is dense in , we say is a Dirichlet algebra.
It can be shown that if an operator 
has as a spectral set, and is a Dirichlet algebra, then has a normal boundary dilation. This generalises Sz.-Nagy's dilation theorem, which can be seen as a consequence of this by letting
See also
- Subdiagonal algebra
References
- {{Citation | last1=Gleason | first1=Andrew M. | authorlink = Andrew Gleason | editor1-last=Morse | editor1-first=Marston | editor2-last=Beurling | editor2-first=Arne | editor3-last=Selberg | editor3-first=Atle | title=Seminars on analytic functions: seminar III : Riemann surfaces ; seminar IV : theory of automorphic functions ; seminar V : analytic functions as related to Banach algebras | publisher=Institute for Advanced Study, Princeton | zbl=0095.10103 | year=1957 | volume=2 | chapter=Function algebras | pages=213–226}}
- {{eom|id=d/d120180|title=Dirichlet algebra|first=T. |last=Nakazi}}
- Completely Bounded Maps and Operator Algebras Vern Paulsen, 2002 {{ISBN|0-521-81669-6}}
- {{citation|last=Wermer|first=John|title=Gleason's work on Banach algebras|department=Andrew M. Gleason 1921–2008|editor-first=Ethan D.|editor-last=Bolker|journal=Notices of the American Mathematical Society|volume=56|issue=10|date=November 2009|pages=1248–1251|url=http://www.ams.org/notices/200910/rtx091001236p.pdf}}.
- Zhengxian
- Zheng Xuan
- Zhengyici Peking Opera Theatre
- Zheng Yi (pirate)
- Zheng Yuanjie
- Zheng Zhenduo
- Zheng Zhen Duo
- Zheng Zhengduo
- Zhengzhou
- Zhengzhou, Henan Province, China
- Zhengzhou Textile Institute
- Zhengzhou University
- Zhengzhou University of Aeronautics
- Zhengzhou University of Light Industry
- Zhengzhou Xinzheng International Airport
- Zhen Ji
- Zhenjiang
- Zhenjiu
- Zhenming zhai
- Zhenotdel
- Zhenping Road station
- Zhenshu
- Zhentil Keep
- Zhen Wenda
- Zhen Wéndá