Remarques sur les {$k((X))$}-algèbres de Banach | Zendy

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Remarques sur les {$k((X))$}-algèbres de Banach

Author(s) -

Bertin Diarra

Publication year - 1995

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1103408717

Subject(s) - ultrametric space , mathematics , banach algebra , pure mathematics , norm (philosophy) , algebra over a field , banach space , metric space , political science , law

Let k be a eld and K = k((X)) be the eld of formal Laurent series over k. Let A be an ultrametric Banach K-algebra; taking appropriated equivalent norm on A, we show that A is obtained by a deformation of the residual k-algebra of A for this norm; given a deformation of a k-algebra, the reverse construction is obvious. The same facts remain true for ultrametric complete Hopf algebras over K. One can prove similar results for ultrametric Banach Lie algebras over K

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