Idempotents in an ultrametric Banach algebra
-
Alain Escassut
alain.escassut@uca.fr
Downloads
DOI:
https://doi.org/10.4067/S0719-06462021000100161Abstract
Let IK be a complete ultrametric field and let \(A\) be a unital commutative ultrametric Banach IK-algebra. Suppose that the multiplicative spectrum admits a partition in two open closed subsets.
Then there exist unique idempotents \(u,\ v\in A\) such that \(\phi(u)=1, \ \phi(v)=0 \ \forall \phi \in U, \ \phi(u)=0 \ \phi(v)=1 \ \forall \phi \in V\). Suppose that IK is algebraically closed. If an element \(x\in A\) has an empty annulus \(r<|\xi-a|<s\) in its spectrum \(sp(x)\), then there exist unique idempotents \(u,\ v\) such that \(\phi(u)=1, \ \phi(v)=0\) whenever \( \phi(x-a)\leq r\) and \(\phi(u)=0, \ \phi(v)=1\) whenever \(\phi(x-a)\geq s\).
Keywords
J. Araujo, Prime and maximal ideals in the spectrum of the ultrametric algebra, Contemporary of the AMS, vol. 704, 2018.
V. Berkovich, Spectral Theory and Analytic Geometry over Non-Archimedean Fields, AMS Survey and Monographs, vol. 33, 1990.
M. Chicourrat, and A. Escassut, “Banach algebras of ultrametric Lipschitzian functions”, Sarajevo Journal of Mathematics, vol. 14, no. 2, pp. 1–12, 2018. (27)
M. Chicourrat, B. Diarra, and A. Escassut, “Finite codimensional maximal ideals in subalgebras of ultrametric uniformly continuous functions”, Bulletin of the Belgium Mathematical Society, vol. 26, no. 3, pp. 413–420, 2019.
M. Chicourrat, and A. Escassut, “Ultrafilters and ultrametric Banach algebras of Lipschitzian functions”, Advances in Operator Theory, vol. 5, no. 1, pp. 115–142, 2020.
M. Chicourrat, and A. Escassut, “A survey and new results on Banach algebras of ultrametric functions”, p-adic Numbers, Ultrametic Analysis and Applications, vol. 12, no. 3, pp. 185–202, 2020.
A. Escassut, Analytic elements in p-adic analysis, World Scientific Publishing, 1995.
A. Escassut, “Algèbres de Banach ultramétriques et algèbres de Krasner-tate”, Astérisque, no. 10, pp. 1-107, 1973.
A. Escassut, Ultrametric Banach algebras, World Scientific Publishing, 2003.
A. Escassut, and N. Mainetti, “Spectrum of ultrametric Banach algebras of strictly differentiable functions”, t Contemporary Mathematics, vol. 704, pp. 139–160, 2018.
A. Escassut, “Survey on the Kakutani problem in p-adic analysis I”, Sarajevo Journal of Mathematics, vol. 15, no. 2, pp. 245–263, 2019.
A. Escassut, “Survey on the Kakutani problem in p-adic analysis II”, Sarajevo Journal of Mathematics, vol. 16, no. 1, pp. 55–70, 2020.
B. Guennebaud, “Alg`ebres localement convexes sur les corps valués”, Bulletin des Sciences Mathématiques, vol. 91, pp. 75–96, 1967.
B. Guennebaud, Sur une notion de spectre pour les algèbres normées ultramétriques, Thèse d‘Etat, Université de Poitiers, 1973.
Ch. E. Rickart, General Theory of Banach Algebras, Krieger Publishing Company, 2002.
P. Salmon, “Sur les séries formelles restrintes”, Bulletin de la Société Mathématique de France, vol. 92, pp. 385–410, 1964.
J. Tate, “Rigid analytic spaces”, Inventiones Mathematicae, vol. 12, pp. 257–289, 1971.
Similar Articles
- Ioannis K. Argyros, Santhosh George, Extended domain for fifth convergence order schemes , CUBO, A Mathematical Journal: Vol. 23 No. 1 (2021)
- Shwet Nisha, P. K. Parida, Super-Halley method under majorant conditions in Banach spaces , CUBO, A Mathematical Journal: Vol. 22 No. 1 (2020)
- Taoufik Chitioui, Khalil Ezzinbi, Amor Rebey, Existence and stability in the α-norm for nonlinear neutral partial differential equations with finite delay , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal
- F. Brackx, H. De Schepper, V. Soucek, Differential forms versus multi-vector functions in Hermitean Clifford analysis , CUBO, A Mathematical Journal: Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal
- Toka Diagana, Khalil Ezzinbi, Mohsen Miraoui, Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory , CUBO, A Mathematical Journal: Vol. 16 No. 2 (2014): CUBO, A Mathematical Journal
- William Greenberg, Michael Williams, Global Solutions of the Enskog Lattice Equation with Square Well Potential , CUBO, A Mathematical Journal: Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal
- Peter Danchev, Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras , CUBO, A Mathematical Journal: Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal
- Patrick Eberlein, Left invariant geometry of Lie groups , CUBO, A Mathematical Journal: Vol. 6 No. 1 (2004): CUBO, A Mathematical Journal
- Feng Qi, The extended mean values: Definition, Properties, Monotonicities, Comparison, Convexities, Generalizations, and Applications , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- Hernán Henríquez M., Comportamiento Asintotico de Semigrupos , CUBO, A Mathematical Journal: Vol. 4 No. 1 (2002): CUBO, Matemática Educacional
<< < 1 2 3 4 5 6 7 8 9 10 > >>
You may also start an advanced similarity search for this article.
Downloads
