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ULTRAFILTERS AND ULTRAMETRIC BANACH ALGEBRAS OF LIPSCHITZ FUNCTIONS
- Source :
- Advances in Operator Theory, Advances in Operator Theory, Tusi Mathematical Research Group, In press, pp.115-142, TUSI Mathematical Group, Advances in Operator Theory, In press, 5, pp.115-142
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- The aim of this paper is to examine Banach algebras of bounded Lipschitz functions from an ultrametric space $$\mathbb {E}$$ to a complete ultrametric field $$\mathbb {K}$$. Considering them as a particular case of what we call C-compatible algebras we study the interactions between their maximal ideals or their multiplicative spectrum and ultrafilters on $$\mathbb {E}$$. We study also their Shilov boundary and topological divisors of zero. Furthermore, we give some conditions on abstract Banach $$\mathbb {K}$$-algebras in order to show that they are algebras of Lipschitz functions on an ultrametric space through a kind of Gelfand transform. Actually, given such an algebra A, its elements can be considered as Lipschitz functions from the set of characters on A provided with some distance $$\lambda _A$$. If A is already the Banach algebra of all bounded Lipschitz functions on a closed subset $$\mathbb {E}$$ of $$\mathbb {K}$$, then the two structures are equivalent and we can compare the original distance defined by the absolute value of $$\mathbb {K}$$, with $$\lambda _A$$.
- Subjects :
- 0209 industrial biotechnology
Pure mathematics
Algebra and Number Theory
010102 general mathematics
Spectrum (functional analysis)
Order (ring theory)
02 engineering and technology
Ultrametric Banach algebras · Ultrafilters · Multiplicative spectrum
Operator theory
Lipschitz continuity
01 natural sciences
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
46S10, 30D35, 30G06
020901 industrial engineering & automation
Bounded function
Banach algebra
Shilov boundary
0101 mathematics
[MATH]Mathematics [math]
Ultrametric space
Analysis
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 2538225X and 26622009
- Database :
- OpenAIRE
- Journal :
- Advances in Operator Theory, Advances in Operator Theory, Tusi Mathematical Research Group, In press, pp.115-142, TUSI Mathematical Group, Advances in Operator Theory, In press, 5, pp.115-142
- Accession number :
- edsair.doi.dedup.....0e85ed30a1d13422f27baf13f8de73fe